Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Incompressible limit of a fluid-particle interaction model
The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity
Influence of bottom topography on long water waves
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy...
Initial-boundary value problem for equations of generalized Newtonian incompressible fluid.
Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case.
Instability of the stationary solutions of generalized dissipative Boussinesq equation
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.
Integration of the equations of gas dynamics for 2.5-dimensional solutions.
Interface cinétique / fluide : Un modèle simplifié
Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case
In this paper we consider weak solutions to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain ( or ). For the critical case we prove the higher integrability of which forms the basis for applying the method of differences in order to get fractional differentiability of . From this we show the existence of second order weak derivatives of .
Invariant tensors and partial differential equations.
Inviscid limit for the 2-D stationary Euler system with arbitrary force in simply connected domains
We study the convergence in the vanishing viscosity limit of the stationary incompressible Navier-Stokes equation towards the stationary Euler equation, in the presence of an arbitrary force term. This requires that the fluid is allowed to pass through some open part of the boundary.
Irregular partially invariant solutions of rank 2 and defect 1 to equations of gas dynamics.