On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

Feireisl, Eduard; Li, Yang

doi:10.1088/1361-6544/ab4c8e

Cited by 25 publications

(10 citation statements)

References 47 publications

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“…When we take no account of the energy equation (1.1) 3 , the system (1.1) is reduced to the well-known compressible isentropic MHD equations. The mathematical results concerning the global existence of (weak, strong or classical) solutions to this model can refer for example to [7,8,10,16,24,26,30]. In contrast to the isentropic case, the non-isentropic model (1.1) is more in line with reality but the problem becomes challenging.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Global existence and decay estimates of strong solutions for compressible non-isentropic magnetohydrodynamic flows with vacuum

Liu¹,

Zhong²

2021

Preprint

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We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids in R 3 . Applying delicate energy estimates, initial layer analysis, and continuation theory, we establish the global existence and uniqueness of strong solutions, which may be of possibly large oscillations, provided that the initial data are of small total energy. In particular, both interior and far field vacuum states are allowed. This improves our previous work [23] where the initial quantity ρ 0 L ∞ + H 0 L 3 must be small enough and the viscosity coefficients should satisfy 3µ > λ. Furthermore, we also derive the algebraic decay estimates of the solution. To our best knowledge, this is the first result on time-decay rates of solutions to the Cauchy problem of multi-dimensional compressible non-isentropic MHD equations with vacuum.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Global existence and decay estimates of strong solutions for compressible non-isentropic magnetohydrodynamic flows with vacuum

Liu¹,

Zhong²

2021

Preprint

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“…In terms of Lions-Feireisl compactness framework for compressible Navier-Stokes equations [8,32], Hu and Wang [14] proved global weak solutions to the 3D initial boundary value problem with finite energy for γ > 3 2 . Non-uniqueness of global-in-time weak solutions for an inviscid fluid in two dimensions was investigated by Feireisl and Li [9]. On the other hand, under the following compatibility condition…”

Section: Introductionmentioning

confidence: 99%

Local well-posedness to the 2D Cauchy problem of full compressible magnetohydrodynamic equations with vacuum at infinity

Chen,

Zhong

2022

Preprint

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This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane R 2 with zero density at infinity. By spatial weighted energy method, we derive the local existence and uniqueness of strong solutions provided that the initial density and the initial magnetic field decay not too slowly at infinity. Note that the initial temperature does not need to decay slowly at infinity. In particular, vacuum states at both the interior domain and the far field are allowed.

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“…For the global existence of weak solutions, we refer to [2,8,14,15] and references therein. There are also some interesting mathematical results concerning the global existence of (weak, strong or classical) solutions to the compressible isentropic MHD equations, please refer to [5,6,9,11,20,23,25].…”

Section: Introductionmentioning

confidence: 99%

Global strong solution for 3D compressible heat-conducting magnetohydrodynamic equations revisited

Liu¹,

Zhong²

2022

Preprint

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We revisit the 3D Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with vacuum as far field density. By delicate energy method, we derive global existence and uniqueness of strong solutions provided that ( ρ 0 L ∞ + 1)) is properly small. In particular, the smallness condition is independent of any norms of the initial data. This work improves our previous results [18,19].

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On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

Cited by 25 publications

References 47 publications

Global existence and decay estimates of strong solutions for compressible non-isentropic magnetohydrodynamic flows with vacuum

Global existence and decay estimates of strong solutions for compressible non-isentropic magnetohydrodynamic flows with vacuum

Local well-posedness to the 2D Cauchy problem of full compressible magnetohydrodynamic equations with vacuum at infinity

Global strong solution for 3D compressible heat-conducting magnetohydrodynamic equations revisited

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