Lp-Lq-Lr estimates and minimal decay regularity for compressible Euler-Maxwell equations

Jiang Xu, Naofumi Mori, Shuichi Kawashima

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9 Citations (Scopus)

Abstract

Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L1(Rn)-L2(Rn). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of Lp(Rn)-Lq(Rn)-Lr(Rn) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler-Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the Lp-version.

Original languageEnglish
Pages (from-to)965-981
Number of pages17
JournalJournal des Mathematiques Pures et Appliquees
Volume104
Issue number5
DOIs
Publication statusPublished - Nov 2015

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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