Research
publications (supported
in part by the NSF grants DMS-0204863 and DMS-0505974)
- The Normal Form of the Navier--Stokes Equations
in Suitable Normed Spaces(With C.
Foias, L. Hoang, and E.
Olson). In preparation.
- On the regularity of the primitive equation with the Dirichlet
boundary condition (with I. Kukavica). Submitted.
- On the regularity of the Navier-Stokes equation in a thin
periodic domain, (with I. Kukavica). Journal
of Differential Equations, Vol 234, 2007, 485-506.
- Sur la régularité des solutions
des équations de Navier-Stokes dans un domaine périodique
de faible épaisseur (with I. Kukavica) C. R. Math.
Acad. Sci. Paris 344 (2007), no. 2, 97--102.
- Regularity of solutions of the primitive equations of the ocean
(with I. Kukavica). Submitted
- Some Mathematical Problems in Geophysical Dynamics (with M. Petcu
and R. Temam). In preparation
- Navier-Stokes equations with regularity in one direction (with I.
Kukavica). Journal of Mathematical
Physics, To appear, (2007).
- Geophysical Dynamics, Encyclopedia of Mathematical Physics (2007)
- Régularité
conditionnelle des équations de Navier-Stokes (with I. Kukavica) C. R. Math. Acad.
Sci. Paris, Vol. 343 (2006), no. 1, pp. 31--36.
- On the solutions to the normal form of
the Navier-Stokes equations (with
C. Foias, L. Hoang, and E.
Olson) Indiana Univ. Math. J.
Vol. 55 (2006), no. 2, pp. 631--686.
- (with I. Kukavica) Regularity of the
Navier-Stokes equation in a thin periodic domain with large data.
(with I. Kukavica) Discrete
Contin. Dyn. Syst. Vol. 16, (2006), no. 1, pp. 67--86.
- One component regularity for the
Navier-Stokes equations. (with I. Kukavica)
. Nonlinearity
19 (2006), no. 2, 453--469.
- A fundamental limit on the heat flux in the control of
incompressible channel flow. (with T. Bewley). IEEE Transactions on Automatic Control, To
appear (2007).
- "A Horizontal hyper-diffusion 2-D
thermocline planetary geostrophic model: well posedness and long time
behavior". (with C. Cao and E. Titi). Submitted.
- "Some Mathematical Problems in
Geophysical
Fluid Dynamics". (with R. Temam). To appear in the Handbook
of
Mathematical Fluid Dynamics . Vol. 3 . S.
Friedlander
and D. Serre Editors, Elsevier.
- "Finite-Dimensional Attractors and
Exponential
Attractors for the Navier-Stokes Equations of Compressible Flow". (with
D. Hoff). SIAM Journal of Mathematical Analysis .
34, (2003), 1040-1063.
- "Existence and uniqueness of optimal
controle of the Navier-Stokes equations". (with T. Bewley and R.
Temam) Comptes Rendus de l'Académie des Sciences.
Série I. Mathématiques t. 330,
(2000), 1007-1011.
- "The Global attractor and finite
determining nodes
for the
Navier-Stokes equations of compressible flow with singular initial
data". (with D. Hoff). Indiana University Mathematics Journal.
49, (2000), 843-889.
- "Compact Attractors for the one
dimensional
compressible Navier-Stokes equation". (with D. Hoff) Comptes
Rendus de l'Académie des Sciences. Série
I. Mathématiques t. 328, (1999), 239-244.
- "On a certain renormalization group
method". Journal of Math. Phys. 41,
(2000), 3290-3299
- "Renormalization group method.
Application to partial differential equations". (with I. Moise ).
J. Dynamics and Diff. Equations. 13, (2001),
275-321
- "A general framework for
robust control in
fluid mechanics". (with T. Bewley and R. Temam). Physica D.
138, 2000, 360-392.
- "Numerical
investigations on stiff differential equations". (with I. Moise, E.
Simmonnet and R. Temam). Journal
of Engineering Mathematics. 34, (1998), 201-214.
- "Asymptotic analysis for the
Navier-Stokes equations in thin domains". (with I. Moise and R.
Temam) . Topolgical Methods in Nonlinear Analysis. 10,
(1997), 249-282.
- "Navier-Stokes equations in thin spherical
shells". (with R. Temam). Contemporary Mathematics, AMS .
Vol 209, (1997), 281-314.
- "On the upper bound on the dimension of
the attractor of the Benard problem". (with A. Miranville).
Russian Journal of Math. Phys. 5, Number 4,
(1997), 489-503.
- "On the two-dimensional Navier-Stokes
equations with the free boundary condition". J. Appl. Math. &
Optimization. 38. (1998), 1-19.
- "Optimal bounds on the
dimension of attractors for the Navier-Stokes equations".
Physica D. 105, (1997), 1-19.
- "Navier Stokes equations in three
dimensional thin domains with various boundary conditions".
Advances in Differential Equations (with R. Temam), 1,
(1996), 499-546.
- "Regularity results
for the stationary primitive equations of the atmosphere and the
ocean". Nonlinear Analysis. Theory, Methods and Applications ,
28, (1997), 289-313.
- "Regularity results
for a Stokes type system". Applicable Analysis ,
58, (1995), 263-293.
- "Regularity results for Stokes type systems
related to climatology". Applied Math. Letters. 8,
(1995), 53-58.