Kato’s type theorems for the convergence of Euler-Voigt equations to Euler equations with drichlet boundary conditions. (English) Zbl 1415.35222

Zang, Aibin

Discrete Contin. Dyn. Syst. 39, No. 9, 4945-4953 (2019).

Summary: After investigating existence and uniqueness of the global strong solutions for Euler-Voigt equations under Dirichlet conditions, we obtain the Kato’s type theorems for the convergence of the Euler-Voigt equations to Euler equations. More precisely, the necessary and sufficient conditions that the solution of Euler-Voigt equation converges to the one of Euler equations, as \( \alpha\to 0 \), can be obtained.

MSC:

35Q30	Navier-Stokes equations
76D05	Navier-Stokes equations for incompressible viscous fluids
76D10	Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

Euler-Voigt equations; Kato’s theorem; nonslip boundary conditions; vanishing filtered parameter limit