Kato's type theorems for the convergence of Euler-Voigt equations to Euler equations with Drichlet boundary conditions

Aibin Zang

doi:10.3934/dcds.2019202

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2019, Volume 39, Issue 9: 4945-4953. Doi: 10.3934/dcds.2019202

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Kato's type theorems for the convergence of Euler-Voigt equations to Euler equations with Drichlet boundary conditions

Aibin Zang

The Center of Applied Mathematics, Yichun University, Yichun, Jiangxi 336000, China

Received: March 2018

Revised: November 2018

Published online: September 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q30, 76D05; Secondary: 75D10.

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