TY - JOUR
T1 - Well-posedness and large time behavior of solutions for the electron inertial Hall-MHD system
AU - Fukumoto, Yasuhide
AU - Zhao, Xiaopeng
N1 - Funding Information:
reading of the paper and helpful suggestions. YF was supported in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Grant No. 16K05476); XZ was supported by the National Natural Science Foundation of China (grant No. 11401258) and China Postdoctoral Science Foundation (grant No. 2015M581689). This work was done when XZ was visiting the Institute of Mathematics for Industry of Kyushu University in 2017. He appreciate the hospitality of IMI.
Publisher Copyright:
© 2019 Khayyam Publishing, Inc.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of elec- tron inertia are studied. First, we establish the existence and uniqueness of local-in-time strong solutions; Then, we prove the existence of global strong solutions under the condition that ∥u 0 ∥ H˙ 1/2 +∥B 0 ∥ H˙ 1/2 +∥∇B 0 ∥ H˙ 1/2 is sufficiently small. Moreover, by applying a cut-off function and gen- eralized energy inequality, we show that the weak solution of electron inertia Hall-MHD system approaches zero as the time t → ∞. Finally, the algebraic decay rate of the weak solution of electron inertia Hall- MHD system is established by using Fourier splitting method and the properties of decay character.
AB - In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of elec- tron inertia are studied. First, we establish the existence and uniqueness of local-in-time strong solutions; Then, we prove the existence of global strong solutions under the condition that ∥u 0 ∥ H˙ 1/2 +∥B 0 ∥ H˙ 1/2 +∥∇B 0 ∥ H˙ 1/2 is sufficiently small. Moreover, by applying a cut-off function and gen- eralized energy inequality, we show that the weak solution of electron inertia Hall-MHD system approaches zero as the time t → ∞. Finally, the algebraic decay rate of the weak solution of electron inertia Hall- MHD system is established by using Fourier splitting method and the properties of decay character.
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M3 - Article
AN - SCOPUS:85061695990
SN - 1079-9389
VL - 24
SP - 31
EP - 68
JO - Advances in Differential Equations
JF - Advances in Differential Equations
IS - 1-2
ER -