Weak Solutions to the Stationary Cahn–Hilliard/Navier–Stokes Equations for Compressible Fluids

Global Weak Solutions to Compressible Navier-Stokes Equations for Quantum Fluids

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations in a three-dimensional torus for large data is proved. The model consists of the mass conservation equation and a momentum balance equation, including a nonlinear thirdorder differential operator, with the quantum Bohm potential, and a density-dependent viscosity. The system has been de...

Weak and Variational Solutions to Steady Equations for Compressible Heat Conducting Fluids

We study steady compressible Navier–Stokes–Fourier system in a bounded three– dimensional domain. Considering a general pressure law of the form p = (γ − 1)̺e, we show existence of a variational entropy solution (i.e. solution satisfying balance of mass, momentum, entropy inequality and global balance of total energy) for γ > 3+ √ 41 8 which is a weak solution (i.e. also the weak formulation of ...

Weak Solutions to the Stationary Incompressible Euler Equations

Helically Symmetric Solutions to the 3-D Navier-Stokes Equations for Compressible Isentropic Fluids

Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for compressible isentropic fluids for any γ > 1 when the Cauchy data are helically symmetric, where the constant γ is the specific heat ratio. Moreover, a new integrability estimate of the density in any neighborhood of the symmetry axis (the singularity axis) is obtained.

Weak and strong solutions of equations of compressible magnetohydrodynamics