Abstract
We identify a class of measure-valued solutions of the barotropic Euler system on a general (unbounded) spatial domain as a vanishing viscosity limit for the compressible Navier–Stokes system. Then we establish the weak (measure-valued)–strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.
Highlights
We consider the compressible Euler system with damping ∂t + divx m = 0, (1)∂tm + divx m ⊗ m + ∇xp( ) + am = 0; (2)here = (t, x) denotes the density, m = m(t, x) the momentum - with the convection that the convective term is equal to zero whenever = 0 - and p = p( ) the pressure
Our goal is to identify a class of generalized - dissipative measure valued (DMV) solutions - for the Euler system (1), (2) as a vanishing viscosity limit of the Navier–Stokes equations
Our goal is to propose an alternative approach based on the concept of dissipative measure-valued solutions and extend the result to a more general class of domains
Summary
here = (t, x) denotes the density, m = m(t, x) the momentum - with the convection that the convective term is equal to zero whenever = 0 - and p = p( ) the pressure. The term am, with a ≥ 0, represents “friction”. We will study the system on the set (t, x) ∈ (0, T ) × Ω, where T > 0 is a fixed time, Ω ⊆ RN with N = 2, 3, can be a bounded or unbounded domain, along with the boundary condition m · n|∂Ω = 0,
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
