TY - JOUR

T1 - The optimal decay estimates on the framework of Besov spaces for the Euler-Poisson two-fluid system

AU - Xu, Jiang

AU - Kawashima, Shuichi

N1 - Funding Information:
The first author 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). He would like to thank Prof. S. Kawashima for giving him an opportunity to work at Kyushu University in Japan. The work is also partially supported by Grant-in-Aid for Scientific Researches (S) 25220702 and (A) 22244009.

PY - 2015/9/20

Y1 - 2015/9/20

N2 - In this paper, we are concerned with the optimal decay estimates for the Euler-Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta-Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of L2 3) (1 & p ;lt& 2) type for the Euler-Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler-Poisson equations, which leads to the sharp decay estimates for velocities. ;copy; 2015 World Scientific Publishing Company.

AB - In this paper, we are concerned with the optimal decay estimates for the Euler-Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta-Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of L2 3) (1 & p ;lt& 2) type for the Euler-Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler-Poisson equations, which leads to the sharp decay estimates for velocities. ;copy; 2015 World Scientific Publishing Company.

KW - Besov spaces

KW - Decay estimates

KW - Euler-Poisson

KW - Littlewood-Paley pointwise estimates

KW - time-weighted energy approaches

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U2 - 10.1142/S0218202515500463

DO - 10.1142/S0218202515500463

M3 - Article

AN - SCOPUS:84941878609

VL - 25

SP - 1813

EP - 1844

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 10

ER -