Global well-posedness and large-time behavior for a special $2\frac{1}{2}$D full compressible viscous non-resistive MHD system

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Hauptverfasser: Zhai, Xiaoping, Zhang, Shunhang
Format: Preprint
Veröffentlicht: 2024
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author Zhai, Xiaoping
Zhang, Shunhang
author_facet Zhai, Xiaoping
Zhang, Shunhang
contents In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing several new unknown quantities and exploiting the intrinsic structure of the system, we prove the global well-posedness of strong solutions for initial data close to a constant equilibrium state. Furthermore, under some suitable additional conditions involving only the low-frequency part of the initial perturbation, we develop a Lyapunov-type energy argument, which yields the optimal time-decay rates of the global solution. To the best of our knowledge, our result is the first one on global solvability to the full compressible, viscous, non-resistive MHD system in multi-dimensional whole space.
format Preprint
id arxiv_https___arxiv_org_abs_2408_07515
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global well-posedness and large-time behavior for a special $2\frac{1}{2}$D full compressible viscous non-resistive MHD system
Zhai, Xiaoping
Zhang, Shunhang
Analysis of PDEs
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing several new unknown quantities and exploiting the intrinsic structure of the system, we prove the global well-posedness of strong solutions for initial data close to a constant equilibrium state. Furthermore, under some suitable additional conditions involving only the low-frequency part of the initial perturbation, we develop a Lyapunov-type energy argument, which yields the optimal time-decay rates of the global solution. To the best of our knowledge, our result is the first one on global solvability to the full compressible, viscous, non-resistive MHD system in multi-dimensional whole space.
title Global well-posedness and large-time behavior for a special $2\frac{1}{2}$D full compressible viscous non-resistive MHD system
topic Analysis of PDEs
url https://arxiv.org/abs/2408.07515