Régularité höldérienne de certains problèmes aux limites elliptiques singuliers
Régularité höldérienne de certains problèmes aux limites elliptiques dégénérés
Régularité précisée des moyennes dans les équations de transport
Régularité lipschitzienne et solutions de l'équation des ondes sur une variété riemannienne compacte
Régularité microlocale pour des problèmes aux limites non linéaires
On étudie la régularité microlocale de type Sobolev au voisinage du bord d’un ouvert de pour des solutions réelles d’un problème aux limites non linéaire non caractéristique dans la zone à comportement linéaire decrite par J. M. Bony : au delà des chocs et en dessous de l’interaction. Pour ces solutions le front d’onde au bord est bien défini et ne contient pas les points de bord elliptiques au sens de Melrose pour le linéarisé sur la solution, si celle-ci vérifie des conditions aux limites régulières....
Régularité microlocale pour des problèmes de Dirichlet non linéaires non caractéristiques d'ordre deux à bord peu régulier
Régularité optimale des solutions de systèmes différentiels et du Laplacien associé; application au ....b.
Régularité de la solution d’un problème unilatéral
Regularity analysis for systems of reaction-diffusion equations
This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi’s method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere...
Regularity and Blow up for Active Scalars
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow...
Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms
We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.
Regularity and free boundary regularity for the Laplacian in Lipschitz and domains.
Regularity and optimal control of quasicoupled and coupled heating processes
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...
Regularity and uniqueness in quasilinear parabolic systems
Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.
Regularity and Uniqueness of Solutions to Boundary Blow-up Problems for the Complex Monge-Ampère Operator
We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder.
Regularity bounds on Zakharov system evolutions.
Regularity criteria for the generalized viscous MHD equations
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity
In this short note we give a link between the regularity of the solution to the 3D Navier-Stokes equation and the behavior of the direction of the velocity . It is shown that the control of in a suitable norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very...
Regularity estimates in Besov spaces for initial-value problems of general parabolic equations.