On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

Jiang, Fei

doi:10.1063/1.4966924

Cited by 21 publications

(6 citation statements)

References 28 publications

(29 reference statements)

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“…However, µ in the system (5.2) can never inhibit the thermal instability due to the absence of κ. Of course, we can rigourously prove that µ can slow down the development of the linear thermal instability in (5.2) in some sense, see [16] on the effect of viscosity on the linear RT instability.…”

Section: Extension To the Magnetic Bénard Problemmentioning

confidence: 94%

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

Jiang

2019

Arch Rational Mech Anal

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We investigate why the non-slip boundary condition for the velocity, imposed in the direction of impressed magnetic fields, can contribute to the magnetic inhibition effect based on the magnetic Rayleigh-Taylor (abbr. NMRT) problem in nonhomogeneous incompressible non-resistive magnetohydrodynamic (abbr. MHD) fluids. Exploiting an infinitesimal method in Lagrangian coordinates, the idea of (equivalent) magnetic tension, and the differential version of magnetic flux conservation, we give an explanation of physical mechanism for the magnetic inhibition phenomenon in a non-resistive MHD fluid. Moreover, we find that the magnetic energy in the non-resistive MHD fluid depends on the displacement of fluid particles, and thus can be regarded as elastic potential energy. Motivated by this observation, we further use the well-known minimum potential energy principle to explain the physical meaning of the stability/instability criteria in the NMRT problem. As a result of the analysis, we further extend the results on the NMRT problem to the stratified MHD fluid case. We point out that our magnetic inhibition theory can be used to explain the inhibition phenomenon of other flow instabilities, such as thermal instability, magnetic buoyancy instability, and so on, by impressed magnetic fields in non-resistive MHD fluids.

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Section: Extension To the Magnetic Bénard Problemmentioning

confidence: 94%

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

Jiang

2019

Arch Rational Mech Anal

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“…At present, the incompressible/compressible MHD equations have been widely investigated; see other studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references cited therein. In particular, for the compressible MHD system, there are many mathematical progress in the existence, stability, and convergence rates of the solutions.…”

Section: Introductionmentioning

confidence: 99%

The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time‐decay rates

Huang

2023

Math Methods in App Sciences

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This paper is concerned with the time‐decay rates of the strong solutions of the three‐dimensional nonisentropic compressible magnetohydrodynamic (MHD) system. First, motivated by Pu and Guo's result [Z. Angew. Math. Phys. 64 (2013) 519–538], we establish the existence result of a unique local‐in‐time strong solution for the MHD system. Then, we derive a priori estimates and use the continuity argument to obtain the global‐in‐time solution, where the initial perturbation is small in H2$$ {H}^2 $$‐norm. Finally, based on Fourier theory and the idea of cancelation of a low‐medium frequent part as in [Sci. China Math. 65 (2022) 1199–1228], we get the optimal time‐decay rates (including highest‐order derivatives) of strong solutions for nonisentropic MHD fluids when the boundedness of L1$$ {L}^1 $$‐norm of the initial perturbation is required. Our result is the first one concerning with the optimal decay estimates of the highest‐order derivatives of the nonisentropic MHD system.

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“…At present, the incompressible/compressible MHD equations have been widely investigated, see 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 and the references cited therein. In particular, for the compressible MHD system, there are many mathematical progress in the existence, stability and convergence rates of the solutions.…”

Section: Introductionmentioning

confidence: 99%

The Cauchy problem for the non-isentropic compressible MHD fluids: optimal time-decay rates

Huang

2022

Preprint

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This paper is concerned with the time-decay rates of the strong solutions of the three dimensional non-isentropic compressible magnetohydrodynamic (MHD) system. First, motivated by Pu–Guo’s result [Z. Angew. Math. Phys. 64 (2013) 519–538], we establish the existence result of a unique local-in-time strong solution for the MHD system. Then, we derive a priori estimates and use the continuity argument to obtain the global-in-time solution, where the initial data should be bounded in L-norm and is small in H-norm. Finally, based on Fourier theory and the idea of cancellation of a low-medium frequent part as in [Sci. China Math. 65 (2022) 1199–1228], we get the optimal time-decay rates (including highest-order derivatives) of strong solutions for non-isentropic MHD fluids. Our result is the first one concerning with the optimal decay estimates of the highest-order derivatives of the non-isentropic MHD system.

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On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

Cited by 21 publications

References 28 publications

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time‐decay rates

The Cauchy problem for the non-isentropic compressible MHD fluids: optimal time-decay rates

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