Examination of Well-Posedness of Multi-Fluid Model.

Well-posedness of a quasilinear hyperbolic fluid model

We replace a Fourier type law by a Cattaneo type law in the derivation of the fundamental equations of fluid mechanics. This leads to hyperbolicly perturbed quasilinear Navier-Stokes equations. For this problem the standard approach by means of quasilinear symmetric hyperbolic systems seems to fail by the fact that finite propagation speed might not be expected. Therefore a somewhat different a...

On well-posedness for a free boundary fluid-structure model

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Well-Posedness for a One-Dimensional Fluid-Particle Interaction Model

The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503–3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singula...

Local Well-posedness of the Multi-layer Shallow Water Model with Free Surface∗

In this paper, we address the question of the hyperbolicity and the local wellposedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this mode...

Well-posedness of Hybrid Systems