L^p-L^q-L^r estimates and minimal decay regularity for compressible Euler-Maxwell equations

2014/10/18 by Jiang Xu, Naofumi Mori, Xu, Jiang +3
Engineering · Mathematics · #35B35 #35B40 #35L40 #82D10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1410.4913

openalex publication_date 2014/10/18 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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 L^p(ℝⁿ)-L^q(ℝⁿ)-L^r(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 L^p-version.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy
• Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application

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