68 citations · 75 across the 8 of their papers we have counts for
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Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems
Jiang Xu, Shuichi Kawashima
Very recently, a new decay framework has been given by [51] for linearized dissipative hyperbolic systems satisfying the Kawashima-Shizuta condition on the framework of Besov space…
-- estimates and minimal decay regularity for compressible Euler-Maxwell equations
Jiang Xu, Naofumi Mori, Shuichi Kawashima
Due to the dissipative structure of \textit{regularity-loss}, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rate…
Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application
Yoshihiro Ueda, Renjun Duan, Shuichi Kawashima
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the…
Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds
Naofumi Mori, Jiang Xu, Shuichi Kawashima
This work first gives the global existence and optimal decay rates of solutions to the classical Timoshenko system on the framework of Besov spaces. Due to the \textit{non-symmetri…
The optimal decay estimates for the Euler-Poisson two-fluid system
Jiang Xu, Shuichi Kawashima
This work is devoted to the optimal decay problem for the Euler-Poisson two-fluid system, which is a classical hydrodynamic model arising in semiconductor sciences. By exploring th…
Global existence and asymptotic decay of solutions to the Non-isentropic Euler-Maxwell system
Yuehong Feng, Shu Wang, Shuichi Kawashima
The non-isentropic compressible Euler-Maxwell system is investigated in in the present paper, and the time decay rate for the global smooth solution is established. It…