TY - JOUR

T1 - Global well-posedness and time-decay of solutions for the compressible Hall-magnetohydrodynamic system in the critical Besov framework

AU - Kawashima, Shuichi

AU - Nakasato, Ryosuke

AU - Ogawa, Takayoshi

N1 - Funding Information:
S. Kawashima is partially supported by JSPS Grant-in-Aid for Scientific Research (B) JP18H01131 . R. Nakasato is supported by JSPS Grant-in-Aid for Scientific Research (S) JP19H05597 and JSPS Grant-in-Aid for Scientific Research (A) JP21H04433 . T. Ogawa is partially supported by JSPS Grant-in-Aid for Scientific Research (S) JP19H05597 and Challenging Research (Pioneering) JP20K20284 .
Publisher Copyright:
© 2022 Elsevier Inc.

PY - 2022/8/15

Y1 - 2022/8/15

N2 - We consider the global existence of solution for the initial value problem for the compressible Hall-magnetohydrodynamic system in the whole space R3. The system consists of a hyperbolic-parabolic system of partial differential equations of the conservation laws type with non-symmetric diffusion. We show the existence of solution as a perturbation from a constant equilibrium state (ρ¯,0,B¯), where ρ¯>0 is a constant density, 0∈R3 is the zero velocity and B¯∈R3 is a constant magnetic field. The time-decay of the solution in the Besov spaces is also established. Our results show the pointwise estimate of the solution in the Fourier space for the linearized Hall-MHD system that related to the result obtained by Umeda–Kawashima–Shizuta [33] for a general class of linear symmetric hyperbolic-parabolic systems with symmetric diffusion. We utilize a systematic use of the product estimates in the Chemin–Lerner spaces and apply the energy method due to Matsumura–Nishida [27].

AB - We consider the global existence of solution for the initial value problem for the compressible Hall-magnetohydrodynamic system in the whole space R3. The system consists of a hyperbolic-parabolic system of partial differential equations of the conservation laws type with non-symmetric diffusion. We show the existence of solution as a perturbation from a constant equilibrium state (ρ¯,0,B¯), where ρ¯>0 is a constant density, 0∈R3 is the zero velocity and B¯∈R3 is a constant magnetic field. The time-decay of the solution in the Besov spaces is also established. Our results show the pointwise estimate of the solution in the Fourier space for the linearized Hall-MHD system that related to the result obtained by Umeda–Kawashima–Shizuta [33] for a general class of linear symmetric hyperbolic-parabolic systems with symmetric diffusion. We utilize a systematic use of the product estimates in the Chemin–Lerner spaces and apply the energy method due to Matsumura–Nishida [27].

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U2 - 10.1016/j.jde.2022.03.017

DO - 10.1016/j.jde.2022.03.017

M3 - Article

AN - SCOPUS:85129281175

SN - 0022-0396

VL - 328

SP - 1

EP - 64

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -