Global existence for two extended Navier-Stokes systems

Global existence for two extended Navier-Stokes systems

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston & Liu [J. Comput. Phys. 199, 221–259, 2004] and by Shirokoff & Rosales [J. Com...

Local and Global Existence for Thecoupled Navier - Stokes - Poisson Problemdonatella

Existence of Global Solutions to Free Boundary Value Problems for Bipolar Navier-stokes-possion Systems

In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP) equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

Existence of Global Weak Solutions to Coupled Navier–stokes–fokker–planck Systems: a Brief Survey

We present a brief survey of recent results concerning the existence of global-in-time weak solutions in a bounded Lipschitz domain in R, d ∈ {2, 3}, to a class of kinetic models for dilute polymeric liquids with noninteracting polymer chains. The mathematical model is a coupled Navier–Stokes–Fokker–Planck system. The velocity and the pressure of the fluid satisfy a Navier–Stokes-like system of...

Existence and bifurcation of Navier-Stokes equations