Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.
We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and...
Existence and stability of solitary waves of Boussinesq-type equations
Existence and stability of steady waves for the Hasegawa-Mima equation.
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and uniqueness for magnetohydrodynamic flows in pipes with viscosity dependent on the temperature.
Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.
Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects.
Existence and Uniqueness of Solutions for the Generalized Korteweg de Vries Equations.
Existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces.
Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...
Existence by minimisation of solitary water waves on an ocean of infinite depth
Existence de nappes de tourbillon pour l'équation d'Euler sur le plan
Existence de solutions avec petite donnée initiale dans pour une équation de Dirac non linéaire
Existence de solutions faibles pour un modèle d'écoulement triphasique en milieu poreux
Existence et comportement asymptotique en temps des solutions de Navier-Stokes Coriolis dans une bande tridimensionnelle
Existence et régularité de la fonction potentiel pour des écoulements subcritiques s'établissant autour d'un corps à singularité conique