Uniform global existence and convergence of Euler-Maxwell systems with small parameters

Victor  Wasiolek

doi:10.3934/cpaa.2016025

Article Contents

2016, Volume 15, Issue 6: 2007-2021. Doi: 10.3934/cpaa.2016025

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Uniform global existence and convergence of Euler-Maxwell systems with small parameters

Victor Wasiolek^1,

1.
20 Rue de Vialle, Lamothe, 43100

Received: March 31, 2015

Revised: March 31, 2016

Published: October 2016

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Abstract

The Euler-Maxwell system with small parameters arises in the modeling of magnetized plasmas and semiconductors. For initial data close to constant equilibrium states, we prove uniform energy estimates with respect to the parameters, which imply the global existence of smooth solutions. Under reasonable assumptions on the convergence of initial conditions, this allows to show the global-in-time convergence of the Euler-Maxwell system as each of the parameters goes to zero.

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Mathematics Subject Classification: 35B40, 35L60.

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