Methods of Vanishing Viscosity for Nonlinear ... - ACMAC

Navier-Stokes Equations =⇒ Euler Equations
Theorem (Chen-Perepelitsa: CPAM 2010)
Let the initial functions (ρ 0 , u 0 ) satisfy the finite-energy
conditions.
Let (ρ ε , m ε ), m ε = ρ ε u ε , be the solution of the Cauchy problem
for the Navier-Stokes equations for each fixed ε > 0.
=⇒ When ε → 0, there exists a subsequence of (ρ ε , m ε ) that
converges strongly almost everywhere to a finite-energy
entropy solution (ρ, m) to the Cauchy problem for
the isentropic Euler equations for any γ > 1.
Gui-Qiang Chen (Oxford) Vanishing Viscosity/Conservation Laws June 20–24, 2011 20 / 40