The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system

Jiang Xu; Shuichi Kawashima

doi:10.1142/S0219891616500193

The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system

Jiang Xu, Shuichi Kawashima

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

Abstract

The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of L^p(Rⁿ)-L^q(Rⁿ)-L^r(Rⁿ) time-decay estimates, we obtain the L¹(R³)-L²(R³) decay rate with the critical regularity (s_c = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Linéaire 29 (2012) 737-759].

Original language	English
Pages (from-to)	719-733
Number of pages	15
Journal	Journal of Hyperbolic Differential Equations
Volume	13
Issue number	4
DOIs	https://doi.org/10.1142/S0219891616500193
Publication status	Published - Dec 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Mathematics(all)

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10.1142/S0219891616500193

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title = "The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system",

abstract = "The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of Lp(Rn)-Lq(Rn)-Lr(Rn) time-decay estimates, we obtain the L1(R3)-L2(R3) decay rate with the critical regularity (sc = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Lin{\'e}aire 29 (2012) 737-759].",

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 World Scientific Publishing Company.",

year = "2016",

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doi = "10.1142/S0219891616500193",

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PY - 2016/12/1

Y1 - 2016/12/1

N2 - The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of Lp(Rn)-Lq(Rn)-Lr(Rn) time-decay estimates, we obtain the L1(R3)-L2(R3) decay rate with the critical regularity (sc = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Linéaire 29 (2012) 737-759].

AB - The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of Lp(Rn)-Lq(Rn)-Lr(Rn) time-decay estimates, we obtain the L1(R3)-L2(R3) decay rate with the critical regularity (sc = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Linéaire 29 (2012) 737-759].

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The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system

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