The frequency-localization technique and minimal decay-regularity for Euler-Maxwell equations

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• 作者：Jiang Xu^a ; ^{jiangxu_79@nuaa.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Shuichi Kawashima^b ; ^{kawashim@math.kyushu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Frequency-localization ; Minimal decay regularity ; Critical Besov spaces ; Euler&ndash ; Maxwell equations
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1537-1554
• 全文大小：436 K

文摘

Dissipative hyperbolic systems of regularity-loss   have been recently received increasing attention. Extra higher regularity is usually assumed to obtain the optimal decay estimates, in comparison with the global-in-time existence of solutions. In this paper, we develop a new frequency-localization time-decay property, which enables us to overcome the technical difficulty and improve the minimal decay-regularity for dissipative systems. As an application, it is shown that the optimal decay rate of n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305613&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305613&_rdoc=1&_issn=0022247X&md5=780c580b85a8b2f983c05d8d4440cc1e" title="Click to view the MathML source">L¹(R³)n>n class="mathContainer hidden">n class="mathCode">n>n>n>–n id="mmlsi2" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305613&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305613&_rdoc=1&_issn=0022247X&md5=7ac44e479b9d7716d576a05e4d85af5c" title="Click to view the MathML source">L²(R³)n>n class="mathContainer hidden">n class="mathCode">n>n>n> is available for Euler–Maxwell equations with the critical regularity n id="mmlsi3" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305613&_mathId=si3.gif&_user=111111111&_pii=S0022247X16305613&_rdoc=1&_issn=0022247X&md5=e90ddd0a7e6ec6a2a25bc19e24edcdf8" title="Click to view the MathML source">s_c=5/2n>n class="mathContainer hidden">n class="mathCode">n>n>n>, that is, the extra higher regularity is not necessary.