Igor Kukavica (Publications)
Research Interests
 Partial differential equations
 Nonlinear dynamics/NavierStokes 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 NavierStokes 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 fluidstructure model,
Nonlinearity (to appear).
110. (with W. Rusin and M. Ziane),
An anisotropic partial regularity criterion for the NavierStokes 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 freesurface Euler equation with surface tension,
Asymptotic Analysis 100 (2016), 6386.
107. (with V. Vicol and F. Wang),
The van Dommelen and Shen singularity in the Prandtl equations,
Advances in Mathematics 307 (2017), 288311.
106. (with V. Vicol and F. Wang),
On the illposedness 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), 185200.
105. (with P. Constantin and V. Vicol),
Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations,
Ann. I. Poincare 33 (2016), 15691588.
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 NavierStokes equations,
J.C. Robinson, J.L. Rodrigo, W. Sadowski, and A. VidalLopez
editors,
London Mathematical Society Lecture Note Series (2016),
7795.
103. (with Z. Bradshaw and Z. Grujic),
Analyticity radii and the NavierStokes equations: recent results and applications,
Recent Progress in the Theory of the Euler and NavierStokes equations,
J.C. Robinson, J.L. Rodrigo, W. Sadowski, and A. VidalLopez
editors,
London Mathematical Society Lecture Note Series (2016),
2236.
102. (with M. Sammartino and M.C. Lombardo),
Zero viscosity limit for analytic solutions of the primitive equations,
Arch. Rational Mech. Anal. 222 (2016), 1445.
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), 523544.
100. (with M. Ignatova and L. Ryzhik),
The Harnack inequality for secondorder parabolic equations with divergencefree drifts of low regularity,
Comm. PDE textbf{41} (2016), 208226.
99. (with F. Wang and M. Ziane),
Persistence of regularity for solutions of the Boussinesq equations in Sobolev spaces,
Adv. Diff. Eq. 21 (2016), 85108.
98. (with Z. Bradshaw and Z. Grujic),
Local analyticity radii of solutions to the 3D NavierStokes equations with analytic forcing,
J. Diff. Eq. 259 (2015), 39553975.
97. (with F. Wang), Weighted decay for the surface quasigeostrophic
equation,
Commun. Math. Sci. 13 (2015), 15991614.
96. (with P. Constantin and V. Vicol),
On the inviscid limit of the NavierStokes equations,
Proceedings of AMS 143 (2015), 30753090.
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), 625668.
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), 241245.
93. (with W. Hu and M. Ziane), Persistence of regularity for a viscous
Boussinesq equations with zero diffusivity,
Asymptotic Analysis 91 (2015), 111124.
92. (with N. GlattHoltz, 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 NavierStokes equations in a bounded domain,
Asymptotic Analysis 90 (2014),
189206.
90. (with N. Masmoudi, V. Vicol, and T. Wong),
On the local wellposedness of the Prandtl and the hydrostatic Euler equations with multiple monotonicity regions,
SIAM J. Math. Anal. 46 (2014), 38653890.
89. (with S. Benachour, W. Rusin, and M. Ziane),
Anisotropic estimates for the twodimensional KuramotoSivashinsky
equation, J. Dynamics Diff. Eq. 26 (2014), 461476.
88. (with W. Rusin and M. Ziane),
A class of large $BMO^{1}$ nonoscillatory data for the NavierStokes equations,
J. Math. Fluid Mechanics 16 (2014), 293305.
87. (with Y. Pei, W. Rusin, and M. Ziane),
Primitive equations with continuous initial data,
Nonlinearity 27 (2014), 11351155.
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), 337358.
85. (with M. Ignatova, I. Lasiecka, and A. Tuffaha),
On wellposedness and small data global existence for an interface damped free boundary fluidstructure model,
Nonlinearity 27 (2014), 467499.
84. (with M. Ignatova and L. Ryzhik),
The Harnack inequality for secondorder elliptic equations with
divergencefree 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 NavierStokes equations with
large data, J. Diff Eq. (to appear).
81. (with W. Rusin and M. Ziane),
Solutions of the NavierStokes equations for large oscillatory
data, Adv. Differential Equations 18 (2013), 549586.
pdf
80. (with A. Mazzucato and A. Tuffaha),
Sharp trace regularity for an anisotropic elasticity system,
Proc. Amer. Math. Soc. 141, 26732682.
pdf
79. (with M. Ignatova), Strong unique continuation
for the NavierStokes equation with nonanalytic forcing,
J. Dynam. Diff. Eq 25 (2013), 115.
pdf
78. (with V. Vicol), On the local existence of analytic solutions
to the Prandtl boundary layer equations,
Commun. Math. Sci 11 (2013), 269292.
pdf
77. (with A. Tuffaha), Regularity of solutions of a free boundary problem of fluidstructure interaction,
Indiana Univ. Math. J. 61 (2012), 18171859.
pdf
76. On the decay of solutions of the NavierStokes 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, 235250.
75. (with A. Tuffaha),
On the 2D free boundary Euler equation,
Evolution Equations and Control Theory 1 (2012), 297314.
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 wellposedness for a free boundary fluidstructure 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), Wellposedness for the compressible NavierStokesLam'e
system with a free interface, Nonlinearity 25 (2012), 31113137.
pdf
70. (with Y. Pei), An estimate on
the parabolic fractal dimension of the singular set for solutions of
the NavierStokes system, Nonlinearity 25 (2012), 27752783.
pdf
69. (with M. Ignatova), Strong unique continuation for higher order elliptic
equations with Gevrey coefficients, J. Diff. Eq. 252
(2012), 29833000.
pdf
68. (with A. Tuffaha), Solutions to a fluidstructure 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 Gevreyclass regularity up to the boundary for the Euler equations, Nonlinearity 4 (2011), 765796.
published version
pdf
66. (with A. Tuffaha and M. Ziane), Strong solutions
to a NavierStokesLame' system on a domain with a nonflat
boundary, Nonlinearity 24 (2011), 159176.
published version
pdf
65. (with E. Reis), Asymptotic expansion for solutions of the
NavierStokes equations with potential forces, J. Diff. Eq.
250 (2011), 607622.
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), 17191746.
published version
pdf
63. Partial regularity for the NavierStokes equations with a force
in a Morrey space, J. Math. Anal. Appl. 374 (2011),
573584.
published version
pdf
62. (with V. Vicol), Domain of analyticity for solutions of the
threedimensional Euler equations in half space, Discrete Contin.
Dynam. Systems 29 (2011), 285303.
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), 639645.
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),
953975.
pdf
59. On regularity for the NavierStokes equations in Morrey
spaces, Discrete
Contin. Dynam. Systems 26 (2010), 13191328.
published version pdf
58. (with A. Tuffaha and M. Ziane), Strong solutions to a
fluid structure interaction system,
Adv. Diff. Eq. 15 (2010), 231254.
pdf
57. Partial regularity results for solutions of the
NavierStokes 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 NavierStokes system, Nonlinearity 22 (2009), 28892900.
published version
pdf
55. (with A. Tuffaha and M. Ziane), Strong solutions to a
nonlinear fluid structure interaction
system, J. Diff. Eq. 247 (2009), 14521478.
published version
pdf
54. On the weighted decay for solutions of the NavierStokes
system, Nonlinear Anal. 70 (2009), 24662470.
published version
pdf
53. (with Vlad Vicol), On the radius of analyticity of solutions
to the threedimensional Euler equations, Proc. Amer.
Math. Soc. 137 (2008), 669677.
published version
pdf
52. (with M. Ziane), Uniform gradient bounds for the primitive
equations of the ocean, Differential Integral
Equations 21 (2008), 837849.
pdf
pdf
51. Regularity for the NavierStokes equations with a solution in
a Morrey space, Indiana Univ. Math. J. 57 (2008), 28432860.
published version
pdf
50. (with Vlad Vicol), On local uniqueness of weak solutions to
the NavierStokes system with $BMO^1$ initial datum,
J. Dynam. Differential Equations 20 (2008), 719732.
published version
pdf
49. On partial regularity for the NavierStokes
equations, Discrete Contin. Dynam. Systems 21 (2008),
717728.
published version
pdf
48. (with M. Ziane), On the Regularity of the
primitive equations of the ocean, Nonlinearity 20 (2007), 27392753.
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), 257260.
published version
pdf
46. (with M. Ziane) NavierStokes 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
NavierStokes equations, Comm. Partial Differential Equations,
32 (2007), 819831.
published version
44.
Loglog convexity and backward uniqueness,
Proc. Amer. Math. Soc. 135 (2007), 24152421.
published version
43. (with M. Ziane) On the regularity of the NavierStokes equation
in a thin periodic domain, J. Differential
Equations 234 (2007), 485506.
published
version
42.
(with M. Ziane)
Sur la re'gularite' des e'quations de NavierStokes dans un domaine mince pe'riodique, C. R.
Acad. Sci. Paris, Ser. I 344 (2007), 97102.
published version
41. (with M. Ziane)
Re'gularite' conditionnelle
des e'quations de NavierStokes, C. R.
Acad. Sci. Paris, Ser. I 343 (2006), 3136.
published version
40. Role of the pressure for validity of the energy equality
for solutions of the NavierStokes equation, J. Dynamics Differential
Equations 18 (2006), 461482.
published version
39. (with M. Ziane) Regularity of the NavierStokes equation in a
thin periodic domain with large data, Discrete Contin. Dyn. Syst.
16 (2006), 6786.
published version
38. Pressure integrability conditions for uniqueness of mild solutions
of the NavierStokes system, J. Diff. Eq. 223 (2006), 427441.
published version
37. (with M. Ziane) One component regularity for the NavierStokes
equation, Nonlinearity 19 (2006), 453469.
published version
36. (with J.J. Torres) Weighted bounds for velocity and vorticity for the
NavierStokes equations, Nonlinearity 19 (2006), 293303.
published version
35.
On Fourier parameterization of global attractors for equations
in one space dimension, Discrete Contin. Dyn. Syst. 13 (2005), 553560.
published version
34. (with M. Malcok) Backward behavior of solutions of the KuramotoSivashinsky equation, J. Math. Anal. Appl. 307 (2005), no. 2, 455464.
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. 12, 4566.
published version
32. Backward uniqueness for solutions of linear parabolic equations, Proc. Amer. Math. Soc. 132 (2004), no. 6, 17551760
published version
31. Spatial complexity of solutions of higher order partial differential equations, Nonlinearity 17 (2004), no. 2, 459476.
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. 23, 473484.
published version
29. On local uniqueness of solutions of the NavierStokes
equations with bounded initial data, J. Diff. Eq
194 (2003), 3950.
published version
(pdf)
28. Length of vorticity nodal sets for solutions of the
NavierStokes system, Comm. PDE 28 (2003), 771793.
published version
(pdf)
27. (with Z. Grujic) A remark on timeanalyticity for the
KuramotoSivashinsky equation,
Nonlinear Analysis 52 (2003), 6978.
published version
(pdf)
26. Spacetime decay for solutions of the NavierStokes
equations. Dedicated to
Professors Ciprian Foias and Roger Temam (Bloomington, IN,
2000), Indiana Univ. Math. J. 50 (2001), Special
Issue, 205222.
published version
(pdf)
25. Interior gradient bounds for the 2D NavierStokes system,
Discrete Contin. Dynam.
Systems 7 (2001), no. 4, 873882
published version
(pdf)
24. (with P. Friz and J. Robinson) Nodal parametrisation of analytic
attractors, Discrete Contin. Dynam. Systems 7 (2001), no. 3, 643657
published version
(pdf)
23. (with C. Foias, M.S. Jolly, and E.S. Titi) The Lorenz equation as
a metaphor for the NavierStokes equations, Discrete
Contin. Dynam. Systems 7 (2001), 403429.
published version
(pdf)
22. Quantitative Uniqueness and Vortex Degree Estimates
for Solutions of the GinzburgLandau Equation,
Electron. J. Differential Equations 2000 (2000), 115
(electronic).
(pdf)
21. A ladder inequality for the NavierStokes
equation, Nonlinearity
13 (2000), 639652.
published version
(pdf)
20. On the dissipative scale for the NavierStokes
equation, Indiana Univ. Math. J. 48 (1999), 10571081.
(pdf)
19. (with Z. Grujic), Space analyticity for the nonlinear heat equation
in a bounded domain, J. Diff. Eq. 154 (1999), 4254.
published version
(pdf)
18. Selfsimilar variables and the
complex GinzburgLandau equation, Comm. PDE 24 (1999), 545562.
(pdf)
17. (with Z. Grujic), Space analyticity for the
NavierStokes and related equations with
initial data in $L^p$, J. Funct. Anal.
152 (1998), 447466.
(pdf)
16. Quantitative uniqueness for second order elliptic
operators, Duke Math. J.
91 (1998), 225240.
(pdf)
15. (with K. Nystrom), Unique continuation on the boundary
for Dini domains, Proceedings of AMS 126 (1998),
441446.
published version
(pdf)
14. Level sets for the stationary GinzburgLandau equation,
Calc. Var. 5 (1997), 511521.
published version
(pdf)
13. (with P. Constantin, C. Foias, and A. Majda), Dirichlet
quotients for periodic 2 dimensional NavierStokes
equations, J. Math Pures Appl. 76 (1997), 125153.
published version
(pdf)
12. (with C. Foias and M. S. Jolly), Localization of
attractors by their analytic properties, Nonlinearity 9
(1996), 15651581.
published version
(pdf)
11. Level sets of the vorticity and the stream function
for the 2D periodic NavierStokes equations with potential
forces, J. Diff. Eq. 126 (1995), 374388.
published version
10. Hausdorff measure of level sets for
solutions of parabolic equations, Internat. Math. Res. Notices
No. 13 (1995) 671682.
(pdf)
9. Nodal volumes for eigenfunctions of
analytic regular
elliptic problems, J. d'Analyse Mathematique 67
(1995), 269280.
(pdf)
8. (with C. Foias), Determining nodes for the
KuramotoSivashinsky equation, J. Dynam. Diff. Eq.
7 (1995), 365373.
published version
(pdf)
7. Hausdorff length of level sets for solutions
of the GinzburgLandau equation, Nonlinearity 8 (1995) , 113129.
published version
(pdf)
6. Oscillations of solutions of the
KuramotoSivashinsky equation, Physica D 76 (1994),
369374.
published
version
(pdf)
5. An absence of certain class of
periodic solutions in the NavierStokes
equations, J. Dynam. Diff. Eq. 6 (1994), 175183.
published version
(pdf)
4. An upper bound for the
winding number for solutions of the
GinzburgLandau equation, Indiana Univ. Math. J.
41 (1992), 825836.
(pdf)
3. On the number of
determining nodes for the GinzburgLandau
equation, Nonlinearity 5 (1992), 9971006.
published version
(pdf)
2. On the behavior of the solutions of the
KuramotoSivashinsky equations for negative
time, J. Math. Anal. Appl. 166 (1992), 601606.
published version
(pdf)
1. On the time analyticity radius of the solutions
of the 2 dimensional NavierStokes
equations, J. Dynam. Diff. Eq. 3 (1991), 611618.
published version
pdf
Last update: December 7, 2016