Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

Advances in Mathematical Fluid Mechanics is a forum for the publication of high quality
monographs, or collections of works, on the mathematical theory of fluid mechanics, with …

We present multicomponent flow models derived from the kinetic theory of gases and
investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial …

Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

We consider barotropic compressible Navier–Stokes equations with density dependent
viscosity coefficients that vanish on vacuum. We prove the stability of weak solutions in …

These notes are devoted to the study of some problems related to shallow-water equations.
In particular, we will review results from derivations of shallow-water systems which depend …

We prove global existence of appropriate weak solutions for the compressible Navier–
Stokes equations for a more general stress tensor than those previously covered by P.-L …

The present paper is dedicated to the global well-posedness issue for the barotropic
compressible Navier–Stokes system in the whole space R^ d with d≧ 2. We aim at …

Abstract The Navier–Stokes–Fourier system describing the motion of a compressible,
viscous and heat conducting fluid is known to possess global-in-time weak solutions for any …

For the three-dimensional full compressible Navier–Stokes system describing the motion of
a viscous, compressible, heat-conductive, and Newtonian polytropic fluid, we establish the …