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

Jiang Xu; Shuichi Kawashima

doi:10.1016/j.jmaa.2016.09.058

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

Jiang Xu, Shuichi Kawashima

Research output: Contribution to journal › Article › peer-review

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Abstract

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 L¹(R³)–L²(R³) is available for Euler–Maxwell equations with the critical regularity s_c=5/2, that is, the extra higher regularity is not necessary.

Original language	English
Pages (from-to)	1537-1554
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	446
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.09.058
Publication status	Published - Feb 15 2017

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.09.058

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title = "The frequency-localization technique and minimal decay-regularity for Euler–Maxwell equations",

abstract = "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 L1(R3)–L2(R3) is available for Euler–Maxwell equations with the critical regularity sc=5/2, that is, the extra higher regularity is not necessary.",

author = "Jiang Xu and Shuichi Kawashima",

note = "Funding Information: J. Xu is partially supported by the National Natural Science Foundation of China ( 11471158 ), the Program for New Century Excellent Talents in University ( NCET-13-0857 ) and the Fundamental Research Funds for the Central Universities ( NE2015005 ). The work is also partially supported by Grant-in-Aid for Scientific Researches (S) 25220702 . Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

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AU - Kawashima, Shuichi

N1 - Funding Information: J. Xu is partially supported by the National Natural Science Foundation of China ( 11471158 ), the Program for New Century Excellent Talents in University ( NCET-13-0857 ) and the Fundamental Research Funds for the Central Universities ( NE2015005 ). The work is also partially supported by Grant-in-Aid for Scientific Researches (S) 25220702 . Publisher Copyright: © 2016 Elsevier Inc.

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N2 - 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 L1(R3)–L2(R3) is available for Euler–Maxwell equations with the critical regularity sc=5/2, that is, the extra higher regularity is not necessary.

AB - 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 L1(R3)–L2(R3) is available for Euler–Maxwell equations with the critical regularity sc=5/2, that is, the extra higher regularity is not necessary.

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

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