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The optimal time‐decay estimate of solutions to two‐fluid Euler‐Maxwell equations in the critical Besov space
Author(s) -
Wu Limiao,
Shi Weixuan,
Xu Jiang
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800272
Subject(s) - besov space , space (punctuation) , euler equations , euler's formula , mathematical analysis , mathematics , type (biology) , constant (computer programming) , physics , computer science , interpolation space , geology , paleontology , biochemistry , chemistry , functional analysis , gene , programming language , operating system
We obtain the optimal time‐decay rate of classical solutions to two‐fluid Euler‐Maxwell equations inR N ( N = 2 , 3 ) , which is a remaining question in the framework of critical Besov space (see [1]). The system is of regularity‐loss , so it is difficult to get decay rates in the solution space. In this paper, the new estimate of L p ‐ L q ‐ L r type and something like “square formula of Duhamel principle” are mainly used. It is shown that in the critical Besov space, the solution decays to constant equilibrium at the rate( 1 + t ) − N 2 ( 1 p − 1 2 )with 1 ≤ p < 6 / 5 if N = 3 and p = 1 if N = 2 .