Published articles in refereed journals
[70] Igor Kukavica, Fanhui Xu, and Mohammed Ziane, Global existence for the stochastic
Navier-Stokes equations with small Lp data. Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), no. 1, 160–189.
[69] Igor Kukavica, David Massat, and Mohammed Ziane Asymptotic properties of the Boussinesq Equations with Dirichlet Boundary Conditions, Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 3060–3081.
[68] Igor Kukavica, Walter Rusin, and Mohammed Ziane, On local regularity conditions for the Navier-Stokes equations. Nonlinearity 32 (2019), no. 6, 1905–1928.
[67] Ibrahim Ekrem, Igor Kukavica, and Mohammed Ziane, Existence of invariant measures for the stochastic damped KdV equation. Indiana Univ. Math. J. 67 (2018), no. 3, 1221—1254.
[66] Igor Kukavica, Kerem Ugurlu, and Mohammed Ziane, On the Galerkin approximation ̃ and strong norm bounds for the stochastic Navier-Stokes equations with multiplicative noise. Differential Integral Equations 31 (2018), no. 3-4, 173–186.
[65] Igor Kukavica, Walter Rusin, and Mohammed Ziane, Localized anisotropic regularity conditions for the Navier-Stokes equations. J. Nonlinear Sci. 27 (2017), no. 6, 1725–1742.
[64] Ibrahim Ekrem, Igor Kukavica, and Mohammed Ziane, Existence of invariant measures for some damped stochastic dispersive equations. C. R. Math. Acad. Sci. Paris 355 (2017), no. 6, 676–679.
[63] Ibrahim Ekrem, Igor Kukavica, and Mohammed Ziane, Existence of invariant measures for the stochastic damped Schr ̈odinger equation. Stoch. Partial Differ. Equ. Anal. Comput. 5 (2017), no. 3, 343–367.
[62] Igor Kukavica, Walter Rusin, and Mohammed Ziane, An anisotropic partial regularity criterion for the Navier-Stokes equations. J. Math. Fluid Mech. 19 (2017), no. 1, 123–133.
[61] Igor Kukavica, Fei Wang, and Mohammed Ziane, Persistence of regularity for the viscous Boussinesq equations in Sobolev spaces, Advances in differential equations 21 (2016), 85–108.
[60] Weiwei Hu, Igor Kukavica, Fei Wang, and Mohammed Ziane, Boussinesq Equations with Zero Viscosity or Zero Difusiivity: a Review, Recent Progress in the Theory of the Euler and Navier-Stokes Equations, Proceedings of the workshop Navier-Stokes equations in Venice”, 2016.
[59] Weiwei Hu, Igor Kukavica, and Mohammed Ziane, Persistence of regularity for the viscous Boussinesq equations with zero diffusivity. Asymptot. Anal. 91 (2015), no. 2, 111–124.
[58] Weiwei Hu, Igor Kukavica, and Mohammed Ziane, Sur l’existence locale pour une ́equation de scalaires actifs. C. R. Math. Acad. Sci. Paris 353 (2015), no. 3, 241–245.
[57] Michele Coti Zelati, Aimin Huang, Igor Kukavica, Roger Temam, and Mohammed Ziane, The primitive equations of the atmosphere in presence of vapour saturation. Non- linearity 28 (2015), no. 3, 625–668.
[56] Igor Kukavica, Walter Rusin, and Mohammed Ziane, A class of large BMO−1 non – oscillatory data for the Navier-Stokes equations. J. Math. Fluid Mech. 16 (2014), no. 2, 293–305.
[55] Said Benachour, Igor Kukavica, Walter Rusin, and Mohammed Ziane, Anisotropic estimates for the two-dimensional Kuramoto-Sivashinsky equation. J. Dynam. Differential Equations 26 (2014), no. 3, 461–476.
[54] Igor Kukavica, Walter Rusin, Yuan Pei, and Mohammed Ziane, Primitive equations with continuous initial data, Nonlinearity 27 (2014), no. 6, 1135–1155.
[53] Nathan Glatt-Holtz, Igor Kukavica, Vlad Vicol, and Mohammed Ziane, Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations. J. Math. Phys. 55 (2014), no. 5, 051504, 34 pp.
[52] Igor Kukavica, Walter Rusin, Mohammed Ziane, A class of solutions of the Navier- Stokes equations with large data. J. Differential Equations 255 (2013), no. 7, 1492–1514.
[51] Igor Kukavica, Walter Rusin, Mohammed Ziane, Solutions of the Navier-Stokes equations for large oscillatory data. Adv. Differential Equations 18 (2013), no. 5-6, 549–586.
[50] Weiwei Hu, Igor Kukavica, and Mohammed Ziane, On the regularity for the Boussinesq equations in a bounded domain, J. Math. Phys. 54, 081507 (2013), 10p.
[49] Jean-Marie Bouteiller, Qui Yumei, Mohammed Ziane., M. Baudry. T.W. Berger. An Online Synaptic Modeling Platform, Engineering in Medicine and Biology Society, 2006, pp. 4155-4158.
[48] Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam, and Mohammed Ziane, Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Nonlinearity 25 (2012), no. 7, 2093–2118.
[47] Mihaela Ignatova, Igor Kukavica, Mohammed Ziane, Local existence of solutions to the free boundary value problem for the primitive equations of the ocean. J. Math. Phys. 53 (2012), no. 10, 103101, 17 pp.
[46] Aseel Farhat, Lee, R., Panetta, R. Edriss Titi, Mohammed Ziane, Long-time behavior
of a two-layer model of baroclinic quasi-geostrophic turbulence. J. Math. Phys. 53 (2012),
no. 11, 115603, 24 pp.
[45] Igor Kukavica, Roger Temam, Vlad Vicol, and Mohammed Ziane, Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. J. Differential Equations 250 (2011), no. 3, 1719–1746.
[44] Igor Kukavica and Amjad Tuffaha, and Mohammed Ziane, Strong Solutions to a Navier-Stokes-Lam ́e System on a Domain with Non-Flat Boundaries. Nonlinearity. Vol. 24 no 1. (2011), pp. 159–176.
[43] Nathan Glatt-Holtz and Mohammed Ziane, Singular perturbation of stochastic differential equations. A renormalization group method approach, Discrete and Continuous Dynamical Systems. Series A, Vol. 26, No 4, 2010.
[42] Igor Kukavica, Roger Temam, Vlad Vicol and Mohammed Ziane, Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data. C.R. Acad. Sci. Paris Vol. 348, no. 11-12, 2010, pp. 639–645.
[41] Igor Kukavica, Amjad Tuffaha, and Mohammed Ziane, Strong solutions to a fluid structure interaction system. Advances in Differential Equations. Vol. 15 (3-4), 2010 pp. 231–254.
[40] Ciprian Foias, Luan Hoang, and Eric Olson, and Mohammed Ziane, The normal form of the Navier–Stokes equations in suitable normed Spaces, ıAnnales de l’Institut Henri Poincare (C) Non Linear Analysis, Vol. 26, No 5, 2009, pp. 1635–1673.
[39] Nathan Glatt-Holtz and Mohammed Ziane, Strong pathwise solutions in H1 of the stochastic Navier-Stokes equation with multiplicative noise, Advances in Differential Equations, Vol. 14, No 5-6, 2009, pp. 567–600.
[38] Igor Kukavica, Amjad Tuffaha and Mohammed Ziane, Strong solutions to a nonlinear fluid structure interaction system. J. Differential Equations Vol. 247, No 5, 2009, pp. 1452–1478.
[37] Theodore Tachim Medjo, Roger Temam, and Mohammed Ziane, Control of fluid flow. Annual Mechanics Reviews, 61, 2008, 23 pages. .
[36] Igor Kukavica and Mohammed Ziane, Uniform bounds on the gradient of the velocity of solutions of the primitive equations. Differential Equations and Integral Equations. Vol. 21, No 9-10, 2008, pp. 837–849.
[35] Nathan Glatt-Holtz and Mohammed Ziane, The stochastic primitive equations in two space dimensions with multiplicative noise. Discrete and Cont. Dyn. Sys. B 10, No. 4, 2008, pp. 801–822.
[34] Igor Kukavica and Mohammed Ziane, On the regularity of the primitive equation with the Dirichlet boundary condition Nonlinearity. 20 No 12, 2007, pp. 2739–2753.
[33] Igor Kukavica and Mohammed Ziane, Navier-Stokes equation with regularity in one direction. Journal of Math. Phys. Journal of Math. Phys., 48 , no. 6, 2007, 10 pages.
[32] Igor Kukavica and Mohammed Ziane, R ́egularit ́e conditonnelle des ́equations de Navier-Stokes, C. R. Math. Acad. Sci. Paris Vol. 343, No 1, 2006, pp. 31–36.
[31] Igor Kukavica and Mohammed Ziane, Regularity of the Navier-Stokes equation in a thin periodic with large data, Journal of Differential Equations. Vol 234 , 2007, 485-506.
[30] Thomas Bewley and Mohammed Ziane, A fundamental limit on the heat flux in the control of incompressible channel flow. IEEE Transactions on Automatic Control, Vol 52, (11), 2007, pp. 2118–2128.
[29] Igor Kukavica and Mohammed Ziane, Sur la r ́egularit ́e des solutions des ́equations de Navier-Stokes dans un domaine p ́eriodique de faible ́epaisseur, C. R. Math. Acad. Sci. Paris. C. R. Math. Acad. Sci. Paris 344 (2007), no. 2, 97-–102 .
[28] Igor Kukavica and Mohammed Ziane, The regularity of solutions of the primitive equations of the ocean in space dimension three. C. R. Math. Acad. Sci. Paris 345 (2007), no. 5, 257—260.
[25] Ciprian Foias, Luan Hoang, Eric Olson, and Mohammed Ziane, On the solutions to the normal form of the Navier-Stokes equations, Indiana University Math Journal, Vol 55, No 2, 2006, pp. 631–686.
[26] Igor Kukavica and Mohammed Ziane, One component regularity for the Navier-Stokes equation, Nonlinearity, Vol 16, No 2 2006, pp. 453–469. .
[27] Igor Kukavica and Mohammed Ziane, Regularity of the Navier-Stokes equation in a thin periodic with large data, Discrete and Continuous Dynamical Systems, Vol 16, No 1, 2006, pp. 67–86.
[25] Ciprian Foias, Luan Hoang, Eric Olson, and Mohammed Ziane, On the solutions to
the normal form of the Navier-Stokes equations, Indiana University Math Journal, Vol 55,
No 2, 2006, pp. 631–686.
[24] Igor Kukavica and Mohammed Ziane, One component regularity for the Navier-Stokes equation, Nonlinearity, Vol 16, No 2 2006, pp. 453–469. .
[23] Igor Kukavica and Mohammed Ziane, Regularity of the Navier-Stokes equation in a thin periodic with large data, Discrete and Continuous Dynamical Systems, Vol 16, No 1, 2006, pp. 67–86.
[22] Changbing Hu, Roger Temam, and Mohammed Ziane, The primitive equations of the large scale ocean under the small depth hypothesis. Discrete and Cont. Dyn. Syst. Vol 9, N0 1, 2003, pp. 97–131.
[21] David Hoff and Mohammed Ziane, Finite dimensional attractors and exponential attractors for the one dimensional compressible Navier-Stokes equations. SIAM J. Math. Analysis. Vol 34, 2003, pp. 1040-1063.
[20] Changbing Hu, Roger Temam, and Mohammed Ziane, Regularity results for linear elliptic problems related to the primitive equations. Chinese Annals of Math., Vol. 23B, No 2, 2002, pp. 277-292.
[19] Ioana Moise and Mohammed Ziane, Renormalization group method Application to partial differential equations. Journal of Dynamics and Diff. Equations. Vol. 13, 2001, pp. 275-321.
[18] Thomas Bewley, Roger Temam, and Mohammed Ziane, A general framework for robust control in fluid mechanics. Physica D, Vol. 138, 2000, pp. 360-392.
[18] David Hoff and Mohammed Ziane, The Global attractor and finite determining nodes for the Navier-Stokes equations of compressible flow with singular initial data. Indiana University Mathematics Journal. Vol. 49, 2000, pp. 843-889.
[16] Thomas Bewley, Roger Temam, and Mohammed Ziane, Existence and Uniqueness of optimal control of the Navier-Stokes equations. Comptes Rendues de l’Acad. Sci. Paris. Vol. 330, 2000, pp. 1007-1011.
[15] Mohammed Ziane, On a certain renormalization group method. Journal of Math Phys. Vol 41, 2000, pp. 3290-3299.
[14] David Hoff and Mohammed Ziane, Compact Attractors for the one dimensional compressible Navier-Stokes equation. Comptes Rendues de l’Acad. Sci. Paris. Vol. 328, 1999, pp. 239-244.
[13] Ioana Moise, Eric Simmonnet Roger Temam, and Mohammed Ziane, Numerical in- vestigations on stiff differential equations. Journal of Engineering Mathematics. Vol. 34, 1998, pp. 201-214.
[12] Mohammed Ziane, On the two-dimensional Navier-Stokes equations with the free boundary condition. J. Appl. Math. & Optimization. Vol. 38 – No 1, 1998, pp. 1-19.
[11] Roger Temam and Mohammed Ziane, Navier-Stokes equations in thin spherical shells.
Contemporary Mathematics, AMS. Vol. 209, 1997, pp. 281-314.
[10] Alain Miranville and Mohammed Ziane, On the upper bound on the dimension of the attractor of the B ́enard problem. Russian Journal of Math. Phys., in honor of M. Vishik. Vol 5, No 4, 1997, pp. 489-503.
[9] Ioana Moise Roger Temam, and Mohammed Ziane, Asymptotic analysis for the Navier- Stokes equations in thin domains. Topological Methods in Nonlinear Analysis. Vol. 10, 1997, pp. 249-282.
[8] Mohammed Ziane, Optimal bounds on the dimension of attractors for the Navier-Stokes equations. Physica D. Vol. 105, 1997, pp. 1-19.
[7] Mohammed Ziane, Regularity results for the stationary primitive equations of the atmosphere and the ocean. Nonlinear Analysis. Theory, Methods and Applications., Vol 28, No 2, 1997, pp. 289-313.
[6] Roger Temam and Mohammed Ziane, Navier-Stokes equations in three dimensional thin domains with various boundary conditions. Advances in Differential Equations, Vol. 1, 1996, pp. 499-546.
[5] Mohammed Ziane, Regularity results for Stokes type systems related to climatology, Applied Math. Letters 8, 1995, pp. 53-58.
[4] Mohammed Ziane, Regularity results for a Stokes type system. Applicable Analysis, Vol. 58, 1995, pp. 263-293.
Book Chapters
[3] Madalina Petcu, Roger Temam, and Mohammed Ziane, Some mathematical problems in fluid dynamics, Handbook of Numerical Analysis, Special volume on Computational Methods for the Ocean and the Atmosphere. 2008, 567-741.
[2] Mohammed Ziane, Geophysical Dynamics, Encyclopedia of Mathematical Physics, Edited by JP Francoise, G Naber and S T Tsou, Elsevier, 2006, pp. 534–539.
[1] Roger Temam and Mohammed Ziane, Some Mathematical Problems in Geophysical Dynamics. Handbook of Mathematical Fluid Dynamics, Vol. III, North-Holland, Amsterdam Elsevier. , 2004, pp. 535–657.