30 research outputs found
Comportement asymptotique pour une inequation parabolique .Applications a diverses equations de la mecanique des fluides visqueux incompressibles
Modeling and Simulation of Thick Sprays through Coupling of a Finite Volume Euler Equation Solver and a Particle Method for a Disperse Phase
We present here the principles of the coupling between an efficient numerical method for hyperbolic systems, namely the FVCF scheme (that is, a finite volume scheme used in the context of non conservative equations arising in multiphase flows), on the one hand; and a particle method for the Vlasov-Boltzmann equation of PIC-DSMC type (that is, in which macroscopic quantities are computed in each cell by adding quantities attached to the particles, and where integrals are computed thanks to a random sampling), on the other hand. Numerical results illustrating this coupling are shown for a problem involving a spray (droplets inside an underlying gas) in a pipe which is modeled by a 1D fluid-kinetic system
Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves
We prove unique continuation properties for solutions of the evolution
Schr\"odinger equation with time dependent potentials. As an application of our
method we also obtain results concerning the possible concentration profiles of
blow up solutions and the possible profiles of the traveling waves solutions of
semi-linear Schr\"odinger equations.Comment: 23 page
Quantum Zakharov Model in a Bounded Domain
We consider an initial boundary value problem for a quantum version of the
Zakharov system arising in plasma physics. We prove the global well-posedness
of this problem in some Sobolev type classes and study properties of solutions.
This result confirms the conclusion recently made in physical literature
concerning the absence of collapse in the quantum Langmuir waves. In the
dissipative case the existence of a finite dimensional global attractor is
established and regularity properties of this attractor are studied. For this
we use the recently developed method of quasi-stability estimates. In the case
when external loads are functions we show that every trajectory from
the attractor is both in time and spatial variables. This can be
interpret as the absence of sharp coherent structures in the limiting dynamics.Comment: 27 page
Finite dimension of global attractors for dissipative equations governing modulated wave
Long-time behaviour for weakly damped driven nonlinear Schr�dinger equations in ? N ,N?3
Singularization of sloshing impacts
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