The Bernoulli manifolds for nonelliptic quasilinear systems of first order and applications in continuum mechanics
The existence and uniqueness of solutions of equations for ideal compressible polytropic fluids.
The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid
The hypersonic Navier-Stokes approximation for the normal shock structure of a perfect gas with the Sutherland viscosity law: Review and extension.
The initial-boundary value problem for the non-barotropic compressible Euler equations : structural-stability and data dependence
The inviscid limit and stability of characteristic boundary layers for the compressible Navier-Stokes equations with Navier-friction boundary conditions
We study boundary layer solutions of the isentropic, compressible Navier-Stokes equations with Navier-friction boundary conditions when the viscosity constants appearing in the momentum equation are proportional to a small parameter . These boundary conditions are characteristic for the underlying inviscid problem, the compressible Euler equations.The boundary condition implies that the velocity on the boundary is proportional to the tangential component of the stress. The normal component of velocity...
The lifespan of spherically symmetric solutions of the compressible Euler equations outside an impermeable sphere
The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class...
The Riemann problem for a class of resonant hyperbolic systems of balance laws
The stability of one dimensional stationary flows of compressible viscous fluids
Time-dependent coupling of Navier–Stokes and Darcy flows
A weak solution of the coupling of time-dependent incompressible Navier–Stokes equations with Darcy equations is defined. The interface conditions include the Beavers–Joseph–Saffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces.
Two problems in homogenization of porous media.
The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related with absorption...