Igor Kukavica (Publications)

Research Interests

Partial differential equations
Nonlinear dynamics/Navier-Stokes Equations

Publications

115. (with G. Camliyurt), Quantitative unique continuation for a parabolic equation, Indiana Univ. Math. J. (to appear).

114. (with G. Camliyurt), A local asymptotic expansion for a solution of the Stokes system, Applied Mathematics and Optimization (to appear).

113. (with I. Ekren and M. Ziane), Existence of invariant measures for the stochastic damped Schrodinger equation, Stochastics and PDE: Analysis and Computation (to appear).

112. (with K. Ugurlu and M. Ziane), On the Galerkin approximation and norm estimates of the stochastic Navier-Stokes equations with multiplicative noise, Integral and Differential Equations (to appear).

111. (with M. Ignatova, I. Lasiecka, and A. Tuffaha), Small data global existence for a fluid-structure model, Nonlinearity (to appear).

110. (with W. Rusin and M. Ziane), An anisotropic partial regularity criterion for the Navier-Stokes equations, J. Math. Fluid Mech. (to appear).

109. (with A. Tuffaha and V. Vicol), On the local existence for the 3D Euler equation with a free interface, Appl. Math. Optim. (to appear).

108. (with M. Ignatova), On the local existence of the free-surface Euler equation with surface tension, Asymptotic Analysis 100 (2016), 63-86.

107. (with V. Vicol and F. Wang), The van Dommelen and Shen singularity in the Prandtl equations, Advances in Mathematics 307 (2017), 288-311.

106. (with V. Vicol and F. Wang), On the ill-posedness of active scalar equations with odd singular kernels, Proceedings of the Eighth Congress of Romanian Mathematicians, New Trends in Differential Equations, Control Theory and Optimization (2016), 185-200.

105. (with P. Constantin and V. Vicol), Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations, Ann. I. Poincare 33 (2016), 1569-1588.

104. (with W. Hu, F. Wang, and M. Ziane), Review for Boussinesq equations with zero viscosity or zero diffusivity, Recent Progress in the Theory of the Euler and Navier-Stokes equations, J.C. Robinson, J.L. Rodrigo, W. Sadowski, and A. Vidal-Lopez editors, London Mathematical Society Lecture Note Series (2016), 77-95.

103. (with Z. Bradshaw and Z. Grujic), Analyticity radii and the Navier-Stokes equations: recent results and applications, Recent Progress in the Theory of the Euler and Navier-Stokes equations, J.C. Robinson, J.L. Rodrigo, W. Sadowski, and A. Vidal-Lopez editors, London Mathematical Society Lecture Note Series (2016), 22-36.

102. (with M. Sammartino and M.C. Lombardo), Zero viscosity limit for analytic solutions of the primitive equations, Arch. Rational Mech. Anal. 222 (2016), 14-45.

101 . (with A. Tuffaha, V. Vicol, and F. Wang), On the existence for the free interface 2D Euler equation with a localized vorticity condition, Appl. Math. Optim. 73 (2016), 523-544.

100. (with M. Ignatova and L. Ryzhik), The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity, Comm. PDE textbf{41} (2016), 208-226.

99. (with F. Wang and M. Ziane), Persistence of regularity for solutions of the Boussinesq equations in Sobolev spaces, Adv. Diff. Eq. 21 (2016), 85-108.

98. (with Z. Bradshaw and Z. Grujic), Local analyticity radii of solutions to the 3D Navier-Stokes equations with analytic forcing, J. Diff. Eq. 259 (2015), 3955-3975.

97. (with F. Wang), Weighted decay for the surface quasi-geostrophic equation, Commun. Math. Sci. 13 (2015), 1599-1614.

96. (with P. Constantin and V. Vicol), On the inviscid limit of the Navier-Stokes equations, Proceedings of AMS 143 (2015), 3075-3090.

95. (with M. Coti Zelati, A. Huang, R. Temam, and M. Ziane), The primitive equations of the atmosphere in presence of vapor saturation, Nonlinearity 28 (2015), 625-668.

94. (with W. Hu and M. Ziane), Sur l'existence locale pour une equation de scalaire actif, C. R. Math. Acad. Sci. Paris 353 (2015), 241-245.

93. (with W. Hu and M. Ziane), Persistence of regularity for a viscous Boussinesq equations with zero diffusivity, Asymptotic Analysis 91 (2015), 111-124.

92. (with N. Glatt-Holtz, V. Vicol, and M. Ziane), Existence and regularity of invariant measures for the three dimensional stochastic primitive equations, J. Math. Phys. 55 (2014), 34 pp.

91. (with V. Vicol), Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain, Asymptotic Analysis 90 (2014), 189-206.

90. (with N. Masmoudi, V. Vicol, and T. Wong), On the local well-posedness of the Prandtl and the hydrostatic Euler equations with multiple monotonicity regions, SIAM J. Math. Anal. 46 (2014), 3865-3890.

89. (with S. Benachour, W. Rusin, and M. Ziane), Anisotropic estimates for the two-dimensional Kuramoto-Sivashinsky equation, J. Dynamics Diff. Eq. 26 (2014), 461-476.

88. (with W. Rusin and M. Ziane), A class of large \$BMO^{-1}\$ non-oscillatory data for the Navier-Stokes equations, J. Math. Fluid Mechanics 16 (2014), 293-305. 87. (with Y. Pei, W. Rusin, and M. Ziane), Primitive equations with continuous initial data, Nonlinearity 27 (2014), 1135-1155.

86. (with A. Tuffaha), A regularity result for the incompressible Euler equation with a free interface, Applied Mathematics and Optimization, Appl. Math. Optim. 69 (2014), 337-358.

85. (with M. Ignatova, I. Lasiecka, and A. Tuffaha), On well-posedness and small data global existence for an interface damped free boundary fluid-structure model, Nonlinearity 27 (2014), 467-499.

84. (with M. Ignatova and L. Ryzhik), The Harnack inequality for second-order elliptic equations with divergence-free drifts, Communications in Math. Sciences (to appear). pdf

83. (with W. Hu and M. Ziane), On the regularity for the Boussinesq equations in a bounded domain, J. Math. Phys. 54 (2013), 10 pp.

82. (with W. Rusin and M. Ziane), A class of solutions of the Navier-Stokes equations with large data, J. Diff Eq. (to appear).

81. (with W. Rusin and M. Ziane), Solutions of the Navier-Stokes equations for large oscillatory data, Adv. Differential Equations 18 (2013), 549-586. pdf

80. (with A. Mazzucato and A. Tuffaha), Sharp trace regularity for an anisotropic elasticity system, Proc. Amer. Math. Soc. 141, 2673-2682. pdf

79. (with M. Ignatova), Strong unique continuation for the Navier-Stokes equation with non-analytic forcing, J. Dynam. Diff. Eq 25 (2013), 1-15. pdf

78. (with V. Vicol), On the local existence of analytic solutions to the Prandtl boundary layer equations, Commun. Math. Sci 11 (2013), 269-292. pdf 77. (with A. Tuffaha), Regularity of solutions of a free boundary problem of fluid-structure interaction, Indiana Univ. Math. J. 61 (2012), 1817-1859. pdf

76. On the decay of solutions of the Navier-Stokes system with potential forces, Mathematical Aspects of Fluid Mechanics, J.C. Robinson, J.L. Rodrigo, and W. Sadowski Editors, London Mathematical Society Lecture Note Series: 402, Cambridge University press, 2012, 235-250.

75. (with A. Tuffaha), On the 2D free boundary Euler equation, Evolution Equations and Control Theory 1 (2012), 297-314. pdf

74. (with M. Ignatova and M. Ziane), Local existence of solutions to the free boundary value problem for the primitive equations of the ocean, Journal of Mathematical Physics 53 (2012), 17pp. (to appear). pdf

73. (with M. Ignatova, I. Lasiecka, and A. Tuffaha), On well-posedness for a free boundary fluid-structure model, J. Math. Phys. 53 (2012), 13 pp. pdf

72. (with C. Doering and E.S. Titi), Introduction to special issue: Incompressible fluids, turbulence and mixing, J. Math. Phys. 11 (2012), 3 pp. pdf

71. (with A. Tuffaha), Well-posedness for the compressible Navier-Stokes-Lam'e system with a free interface, Nonlinearity 25 (2012), 3111-3137. pdf

70. (with Y. Pei), An estimate on the parabolic fractal dimension of the singular set for solutions of the Navier-Stokes system, Nonlinearity 25 (2012), 2775-2783. pdf

69. (with M. Ignatova), Strong unique continuation for higher order elliptic equations with Gevrey coefficients, J. Diff. Eq. 252 (2012), 2983-3000. pdf

68. (with A. Tuffaha), Solutions to a fluid-structure interaction free boundary problem, Discrete Contin. Dyn. Syst. 32 (2012), no. 4, 1355–1389. published version  pdf

67. (with V. Vicol), On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations, Nonlinearity 4 (2011), 765-796. published version  pdf

66. (with A. Tuffaha and M. Ziane), Strong solutions to a Navier-Stokes-Lame' system on a domain with a non-flat boundary, Nonlinearity 24 (2011), 159-176. published version  pdf

65. (with E. Reis), Asymptotic expansion for solutions of the Navier-Stokes equations with potential forces, J. Diff. Eq. 250 (2011), 607-622. published version  pdf

64. (with R. Temam, V. Vicol, and M. Ziane), Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain, J. Diff. Eq. 250 (2011), 1719-1746. published version  pdf

63. Partial regularity for the Navier-Stokes equations with a force in a Morrey space, J. Math. Anal. Appl. 374 (2011), 573-584. published version  pdf

62. (with V. Vicol), Domain of analyticity for solutions of the three-dimensional Euler equations in half space, Discrete Contin. Dynam. Systems 29 (2011), 285-303. published version  pdf

61. (with R. Temam, V. Vicol, and M. Ziane), Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain, C. R. Math. Acad. Sci. Paris 348 (2010), 639-645. published version pdf

60. (with M. Ignatova), Unique continuation and complexity of solutions to parabolic partial differential equations with Gevrey coefficients, Adv. Diff. Eq. 15 (2010), 953-975. pdf

59. On regularity for the Navier-Stokes equations in Morrey spaces, Discrete Contin. Dynam. Systems 26 (2010), 1319-1328. published version pdf

58. (with A. Tuffaha and M. Ziane), Strong solutions to a fluid structure interaction system, Adv. Diff. Eq. 15 (2010), 231-254. pdf

57. Partial regularity results for solutions of the Navier-Stokes system, J. Rodrigo and J.C. Robinson editors, Proceedings of the workshop on ``Partial differential equations and fluid mechanics,'' Warwick, 2009. pdf

56. The fractal dimension of the singular set for solutions of the Navier-Stokes system, Nonlinearity 22 (2009), 2889-2900. published version  pdf

55. (with A. Tuffaha and M. Ziane), Strong solutions to a nonlinear fluid structure interaction system, J. Diff. Eq. 247 (2009), 1452-1478. published version  pdf

54. On the weighted decay for solutions of the Navier-Stokes system, Nonlinear Anal. 70 (2009), 2466-2470. published version  pdf

53. (with Vlad Vicol), On the radius of analyticity of solutions to the three-dimensional Euler equations, Proc. Amer. Math. Soc. 137 (2008), 669-677. published version  pdf

52. (with M. Ziane), Uniform gradient bounds for the primitive equations of the ocean, Differential Integral Equations 21 (2008), 837-849. pdf  pdf

51. Regularity for the Navier-Stokes equations with a solution in a Morrey space, Indiana Univ. Math. J. 57 (2008), 2843-2860. published version  pdf

50. (with Vlad Vicol), On local uniqueness of weak solutions to the Navier-Stokes system with \$BMO^-1\$ initial datum, J. Dynam. Differential Equations 20 (2008), 719-732. published version  pdf

49. On partial regularity for the Navier-Stokes equations, Discrete Contin. Dynam. Systems 21 (2008), 717-728. published version  pdf

48. (with M. Ziane), On the Regularity of the primitive equations of the ocean, Nonlinearity 20 (2007), 2739-2753. published version  pdf

47. (with M. Ziane), The regularity of solutions of the primitive equations of the ocean in space dimension three, C. R. Math. Acad. Sci. Paris 345 (2007), 257-260. published version  pdf

46. (with M. Ziane) Navier-Stokes equation with regularity in one direction, J. Math. Phys. 48 (2007), 10pp. published version

45. (with J.J. Torres) Weighted \$L^p\$ decay for solutions of the Navier-Stokes equations, Comm. Partial Differential Equations, 32 (2007), 819­831. published version

44. Log-log convexity and backward uniqueness, Proc. Amer. Math. Soc. 135 (2007), 2415-2421. published version

43. (with M. Ziane) On the regularity of the Navier-Stokes equation in a thin periodic domain, J. Differential Equations 234 (2007), 485-506. published version

42. (with M. Ziane) Sur la re'gularite' des e'quations de Navier-Stokes dans un domaine mince pe'riodique, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 97-102. published version

41. (with M. Ziane) Re'gularite' conditionnelle des e'quations de Navier-Stokes, C. R. Acad. Sci. Paris, Ser. I 343 (2006), 31-36. published version

40. Role of the pressure for validity of the energy equality for solutions of the Navier-Stokes equation, J. Dynamics Differential Equations 18 (2006), 461-482. published version

39. (with M. Ziane) Regularity of the Navier-Stokes equation in a thin periodic domain with large data, Discrete Contin. Dyn. Syst. 16 (2006), 67-86. published version

38. Pressure integrability conditions for uniqueness of mild solutions of the Navier-Stokes system, J. Diff. Eq. 223 (2006), 427-441. published version

37. (with M. Ziane) One component regularity for the Navier-Stokes equation, Nonlinearity 19 (2006), 453-469. published version

36. (with J.J. Torres) Weighted bounds for velocity and vorticity for the Navier-Stokes equations, Nonlinearity 19 (2006), 293-303. published version

35. On Fourier parameterization of global attractors for equations in one space dimension, Discrete Contin. Dyn. Syst. 13 (2005), 553-560. published version

34. (with M. Malcok) Backward behavior of solutions of the Kuramoto-Sivashinsky equation, J. Math. Anal. Appl. 307 (2005), no. 2, 455-464. published version

33. (with J. Robinson) Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem, Phys. D 196 (2004), no. 1-2, 45-66. published version

32. Backward uniqueness for solutions of linear parabolic equations, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1755-1760 published version

31. Spatial complexity of solutions of higher order partial differential equations, Nonlinearity 17 (2004), no. 2, 459-476. published version

30. Fourier parameterization of attractors for dissipative equations in one space dimension. Special issue dedicated to Victor A. Pliss on the occasion of his 70th birthday, J. Dynam. Differential Equations 15 (2003), no. 2-3, 473-484. published version

29. On local uniqueness of solutions of the Navier-Stokes equations with bounded initial data, J. Diff. Eq 194 (2003), 39-50. published version (pdf)

28. Length of vorticity nodal sets for solutions of the Navier-Stokes system, Comm. PDE 28 (2003), 771-793. published version (pdf)

27. (with Z. Grujic) A remark on time-analyticity for the Kuramoto-Sivashinsky equation, Nonlinear Analysis 52 (2003), 69-78. published version (pdf)

26. Space-time decay for solutions of the Navier-Stokes equations. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000), Indiana Univ. Math. J. 50 (2001), Special Issue, 205-222. published version (pdf)

25. Interior gradient bounds for the 2D Navier-Stokes system, Discrete Contin. Dynam. Systems 7 (2001), no. 4, 873-882 published version (pdf)

24. (with P. Friz and J. Robinson) Nodal parametrisation of analytic attractors, Discrete Contin. Dynam. Systems 7 (2001), no. 3, 643-657 published version (pdf)

23. (with C. Foias, M.S. Jolly, and E.S. Titi) The Lorenz equation as a metaphor for the Navier-Stokes equations, Discrete Contin. Dynam. Systems 7 (2001), 403-429. published version (pdf)

22. Quantitative Uniqueness and Vortex Degree Estimates for Solutions of the Ginzburg-Landau Equation, Electron. J. Differential Equations 2000 (2000), 1-15 (electronic). (pdf)

21. A ladder inequality for the Navier-Stokes equation, Nonlinearity 13 (2000), 639-652. published version (pdf)

20. On the dissipative scale for the Navier-Stokes equation, Indiana Univ. Math. J. 48 (1999), 1057-1081. (pdf)

19. (with Z. Grujic), Space analyticity for the nonlinear heat equation in a bounded domain, J. Diff. Eq. 154 (1999), 42-54. published version (pdf)

18. Self-similar variables and the complex Ginzburg-Landau equation, Comm. PDE 24 (1999), 545-562. (pdf)

17. (with Z. Grujic), Space analyticity for the Navier-Stokes and related equations with initial data in \$L^p\$, J. Funct. Anal. 152 (1998), 447-466. (pdf)

16. Quantitative uniqueness for second order elliptic operators, Duke Math. J. 91 (1998), 225-240. (pdf)

15. (with K. Nystrom), Unique continuation on the boundary for Dini domains, Proceedings of AMS 126 (1998), 441-446. published version (pdf)

14. Level sets for the stationary Ginzburg-Landau equation, Calc. Var. 5 (1997), 511-521. published version (pdf)

13. (with P. Constantin, C. Foias, and A. Majda), Dirichlet quotients for periodic 2 dimensional Navier-Stokes equations, J. Math Pures Appl. 76 (1997), 125-153. published version (pdf)

12. (with C. Foias and M. S. Jolly), Localization of attractors by their analytic properties, Nonlinearity 9 (1996), 1565-1581. published version (pdf)

11. Level sets of the vorticity and the stream function for the 2D periodic Navier-Stokes equations with potential forces, J. Diff. Eq. 126 (1995), 374-388. published version

10. Hausdorff measure of level sets for solutions of parabolic equations, Internat. Math. Res. Notices No. 13 (1995) 671-682. (pdf)

9. Nodal volumes for eigenfunctions of analytic regular elliptic problems, J. d'Analyse Mathematique 67 (1995), 269-280. (pdf)

8. (with C. Foias), Determining nodes for the Kuramoto-Sivashinsky equation, J. Dynam. Diff. Eq. 7 (1995), 365-373. published version (pdf)

7. Hausdorff length of level sets for solutions of the Ginzburg-Landau equation, Nonlinearity 8 (1995) , 113-129. published version (pdf)

6. Oscillations of solutions of the Kuramoto-Sivashinsky equation, Physica D 76 (1994), 369-374. published version (pdf)

5. An absence of certain class of periodic solutions in the Navier-Stokes equations, J. Dynam. Diff. Eq. 6 (1994), 175-183. published version (pdf)

4. An upper bound for the winding number for solutions of the Ginzburg-Landau equation, Indiana Univ. Math. J. 41 (1992), 825-836. (pdf)

3. On the number of determining nodes for the Ginzburg-Landau equation, Nonlinearity 5 (1992), 997-1006. published version (pdf)

2. On the behavior of the solutions of the Kuramoto-Sivashinsky equations for negative time, J. Math. Anal. Appl. 166 (1992), 601-606. published version (pdf)

1. On the time analyticity radius of the solutions of the 2 dimensional Navier-Stokes equations, J. Dynam. Diff. Eq. 3 (1991), 611-618. published version pdf

Last update: December 7, 2016