Incompressible Limit of the Nonisentropic Ideal Magnetohydrodynamic Equations

Jiang, Song; Ju, Qiangchang; Li, Fucai

doi:10.1137/15m102842x

Cited by 30 publications

(10 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and different domains (whole space, periodic domain, bounded domain, etc.). Among them, we mention Ukai [33] (initial layer in R d ), Schochet [30] and Grenier [10] (fast acoustic waves on torus), Lions and Masmoudi [24] (incompressible limit for global in time weak solutions of isentropic compressible Navier-Stokes equations), Métivier and Schochet [27,29] (incompressible limit for non-isentropic Euler equations), Alazard [2] (low Mach number limit of the full Navier-Stokes equations in R d ), Jiang-Ju-Li [15] (incompressible limit for non-isentropic MHD equations in [16] (low Mach number limit of the full MHD equations in R d ).…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

Luo¹,

Ma²

2021

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

In this paper we study the incompressible limit of the compressible inertial Qian-Sheng model for liquid crystal flow. We first derive the uniform energy estimates on the Mach number for both the compressible system and its differential system with respect to time under uniformly in small initial data. Then, based on these uniform estimates, we pass to the limit in the compressible system as → 0, so that we establish the global classical solution of the incompressible system by compactness arguments. We emphasize that, on global in time existence of the incompressible inertial Qian-Sheng model under small size of initial data, the range of our assumptions on the coefficients are significantly enlarged, comparing to the results of De Anna and Zarnescu's work [6]. Moreover, we also obtain the convergence rates associated with L 2norm with well-prepared initial data.

show abstract

Section: Remarkmentioning

confidence: 99%

“…From taking the inner product of third equation of (13) withQ, and using the third equation of (15), it infer that…”

mentioning

confidence: 99%

Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

Luo¹,

Ma²

2021

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

show abstract

“…For the one dimensional Euler equations, the low Mach number limit has been proved under the B.V. space in [7]. For other related fluid models and problems, see [5,11,22,26,27,30,31,33,34,36] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

Wang

Xiang

2019

Preprint

View full text Add to dashboard Cite

In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with extra force to the corresponding incompressible flow, which is free from the extra force effect, as the Mach number goes to zero. The limit is on the Hölder space and is unique. Moreover, the convergence rate is of order ε 2 , which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

show abstract

“…The compressible MHD system is a combination of the compressible Navier‐Stokes equations of fluid dynamics and Maxwells equations of electromagnetism. There have been a number of studies on MHD by physicists and mathematicians because of their physical importance, complexity, rich phenomena, and mathematical challenging; see and references cited therein. The one‐dimensional problem has been studied in many papers, for example, and so on.…”

Section: Introductionmentioning

confidence: 99%

A new blowup criterion for strong solutions to the three‐dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain

Chen

Hou

Zhu

2017

Math Methods in App Sciences

View full text Add to dashboard Cite

A new blowup criterion for strong solutions to the three-dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain Communicated by Z. XinIn this paper, we establish a new blowup criterions for the strong solution to the Dirichlet problem of the threedimensional compressible MHD system with vacuum. Specifically, we obtain the blowup criterion in terms of the concentration of density in BMO norm or the concentration of the integrability of the magnetic field at the first singular time. The BMO-type estimate for the LamK e system (2.6) and a variant of the Brezis-Waigner's inequality (2.3) play a critical role in the proof. which implies C 1 3 > 0. The compressible MHD system (1.1) is a combination of the compressible Navier-Stokes equations of fluid dynamics and Maxwells equations of electromagnetism. There have been a number of studies on MHD by physicists and mathematicians because of their

show abstract

Incompressible Limit of the Nonisentropic Ideal Magnetohydrodynamic Equations

Cited by 30 publications

References 32 publications

Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

A new blowup criterion for strong solutions to the three‐dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain

Contact Info

Product

Resources

About