We consider the motion of a viscous compressible fluid confined to a physical space with a time dependent kinematic boundary. We suppose that the characteristic speed of the fluid is dominated by the speed of sound and perform the low Mach number limit in the framework of weak solutions. The standard incompressible Navier-Stokes system is identified as the target problem.

New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.

We propose a mixed numerical method for solving the compressible Navier-Stokes system and study its convergence and stability with respect to the physical domain. The numerical solutions are shown to converge, up to a subsequence, to a weak solution of the problem posed on the limit domain.

A full Navier-Stokes solver has been used t o model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to held at the AIAA 25th Aerospace Sciences Meeting. "Jones" airfoils have been inves...

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of [7] for the system on moving domain and use it to prove the weak-strong uniqueness property.

Abstract. We investigate the use of compactly supported divergence-free wavelets for the representation of solutions of the Navier-Stokes equations. After reviewing the theoretical construction of divergence-free wavelet vectors, we present in detail the bases and corresponding fast algorithms for two and three-dimensional incompressible flows. We also propose a new method to practically comput...

We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier–Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic “galloping”, or “pulsating”, solutions, in agreement with physical and numerical observation. The analysis is by pointwise semigroup techniques introduced by the authors and collaborators in pr...

We consider the full system of compressible Navier-Stokes equations for heat conducting fluid. We show that the temperature is uniformly positive for t ≥ t0 (for any t0 > 0) for any solutions with finite initial entropy. The assumptions on the viscosity and conductivity coefficients are minimal (for instance, the solutions constructed by E. Feireisl in [2] verify all the requirements).

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained.

This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.