Sur l'existence et la régularité de solutions radiales pour des équations de type Monge-Ampère complexe.
Sur quelques résultats récents de mécanique des fluides
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.
Temps de vie des solutions régulières des équations d'Euler compressibles axisymétriques en dimension deux.
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary value problem of the equations with nonnegative characteristic form.
The Calderón-Zygmund theory for elliptic problems with measure data
We consider non-linear elliptic equations having a measure in the right-hand side, of the type and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calderón-Zygmund theory for the problem. All the regularity results presented in this paper are provided together with explicit local a priori estimates.
The Cauchy problem for the two dimensional Euler–Poisson system
The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system....
The critical nonlinear wave equation in two space dimensions
Extending our previous work, we show that the Cauchy problem for wave equations with critical exponential nonlinearities in 2 space dimensions is globally well-posed for arbitrary smooth initial data.
The Dirichlet problem for the minimal surface equation with Lipschitz continuous boundary data.
The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input state” map in -norms is established. A structure of the reachable sets for arbitrary is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input → state" map in L2-norms is established. A structure of the reachable sets for arbitrary T>0 is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The existence of solutions for elliptic systems with nonuniform growth
We study the Dirichlet problems for elliptic partial differential systems with nonuniform growth. By means of the Musielak-Orlicz space theory, we obtain the existence of weak solutions, which generalizes the result of Acerbi and Fusco [1].
The first initial-boundary value problem for quasilinear second order parabolic equations
The generalized Dirichlet problem for equations of Monge-Ampère type
The inhomogeneous dam problem with discontinuous permeability
The interface crack with Coulomb friction between two bonded dissimilar elastic media
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.
The Kolmogorov equation with time-measurable coefficients.
The local boundary regularity of the solution of the -equation