THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN*

doi:10.1007/s10473-024-0522-3

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1997-2018.doi: 10.1007/s10473-024-0522-3

THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*

Zefu Feng^†, Jing Jia

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

收稿日期:2022-07-14 修回日期:2024-05-15 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Zefu Feng, E-mail,: zefufeng@mails.ccnu.edu.cn
作者简介:Jing Jia, E-mail,: jj9702112022@163.com
基金资助:
National Natural Science Foundation of China (12101095), the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX0949, 2022NSCQ-MSX2878, CSTC2021jcyj-msxmX0224), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202100517, KJQN202300542, KJQN202100511) the Research Project of Chongqing Education Commission (CXQT21014) and the grant of Chongqing Young Experts' Workshop.

THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*

Zefu Feng^†, Jing Jia

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2022-07-14 Revised:2024-05-15 Online:2024-10-25 Published:2024-10-22
Contact: †Zefu Feng, E-mail,: zefufeng@mails.ccnu.edu.cn
About author:Jing Jia, E-mail,: jj9702112022@163.com
Supported by:
National Natural Science Foundation of China (12101095), the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX0949, 2022NSCQ-MSX2878, CSTC2021jcyj-msxmX0224), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202100517, KJQN202300542, KJQN202100511) the Research Project of Chongqing Education Commission (CXQT21014) and the grant of Chongqing Young Experts' Workshop.

摘要/Abstract

摘要： In this paper, we consider a model of compressible isentropic two-fluid magnetohydrodynamics without resistivity in a strip domain in three dimensional space. By exploiting the two-tier energy method developed in [Anal PDE, 2013, 6: 1429-1533], we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. Compared to the work of Tan and Wang [SIAM J Math Anal, 2018, 50: 1432-1470], we need to overcome the difficulties caused by particles.

关键词: two-fluid magnetohydrodynamics, global well-posedness, compressiblility

Abstract: In this paper, we consider a model of compressible isentropic two-fluid magnetohydrodynamics without resistivity in a strip domain in three dimensional space. By exploiting the two-tier energy method developed in [Anal PDE, 2013, 6: 1429-1533], we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. Compared to the work of Tan and Wang [SIAM J Math Anal, 2018, 50: 1432-1470], we need to overcome the difficulties caused by particles.

Key words: two-fluid magnetohydrodynamics, global well-posedness, compressiblility

中图分类号:

35Q35

Zefu Feng, Jing Jia. THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*[J]. 数学物理学报(英文版), 2024, 44(5): 1997-2018.

Zefu Feng, Jing Jia. THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1997-2018.

参考文献

[1] Agmon S, Douglis A, Nirenberg L.Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II. Comm Pure Appl Math, 1964, 17: 35-92
[2] Boardman N, Lin H, Wu J.Stabilization of a background magnetic field on a 2 dimensional magnetohy- drodynamic ow. SIAM J Math Anal, 2020, 52: 5001-5035
[3] Carrillo J A, Goudon T.Stability and asymptotic analysis of a uid-particle interaction model. Comm Partial Differential Equations, 2006, 31: 1349-1379
[4] Fan J, Jiang S, Nakamura G.Stability of weak solutions to equations of magnetohydrodynamics with Lebesgue initial data. J Differential Equations, 2011, 251: 2025-2036
[5] Guo Y, Tice I.Almost exponential decay of periodic viscous surface waves without surface tension. Arch Ration Mech Anal, 2013, 207: 459-531
[6] Guo Y, Tice I.Decay of viscous surface waves without surface tension in horizontally infinite domains. Anal PDE, 2013, 6: 1429-1533
[7] Hong G Y, Hou X F, Peng H Y, Zhu C J.Global existence for a class of large solutions to three-dimensional compressible magnetohydrodynamic equations with vacuum. SIAM J Math Anal, 2017, 49: 2409-2441
[8] Hu X.Global existence for two dimensional compressible magnetohydrodynamic ows with zero magnetic diffusivity. arXiv:1405.0274
[9] Hu X, Wang D.Compactness of weak solutions to the three-dimensional compressible magnetohydrody- namic equations, J Differential Equations, 2008, 245: 2176-2198
[10] Hu X, Wang D.Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic ows. Arch Ration Mech Anal, 2010, 197: 203-238
[11] Ishii M.Thermo- uid Dynamic Theory of Two- uid Flow. Paris: Eyrolles, 1975
[12] Jiang P.Global well-posedness and large time behavior of classical solutions to the Vlasov-Fokker-Planck and magnetohydrodynamics equations. J Differential Equations, 2017, 262: 2961-2986
[13] Li H L, Xu X, Zhang J.Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum. SIAM J Math Anal, 2013, 45: 1356-1387
[14] Lin F, Xu L, Zhang P.Global small solutions of 2-D incompressible MHD system. J Differential Equations, 2015, 259: 5440-5485
[15] Ma L, Guo B, Shao J.Global weak solutions to some two- uid models with magnetic field. arX- iv:2103.08344v2
[16] Ren X, Wu J, Xiang Z, Zhang Z.Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion. J Funct Anal, 2014, 267: 503-541
[17] Ren X, Xiang Z, Zhang Z.Global well-posedness for the 2D MHD equations without magnetic diffusion in a strip domain. Nonlinearity, 2016, 29: 1257-1291
[18] Ruan L, Trakhinin Y. Shock waves and characteristic discontinuities in ideal compressible two- uid MHD. Z Angew Math Phys, 2019, 70: Art 17
[19] Strain R M, Guo Y.Almost exponential decay near Maxwellian. Comm Partial Differential Equations, 2006, 31: 417-429
[20] Tan Z, Wang Y.Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems. SIAM J Math Anal, 2018, 50: 1432-1470
[21] Vasseur A, Wen H, Yu C.Global weak solution to the viscous two- uid model with finite energy. J Math Pures Appl, 2019, 125: 247-282
[22] Wen H, Zhu L.Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field. J Differential Equations, 2018, 264: 2377-2406
[23] Wu J,Wu Y.Global small solutions to the compressible 2d magnetohydrodynamic system without magnetic diffusion. Adv Math, 2017, 310: 759-888
[24] Yin H, Zhu L. Convergence rate of solutions toward stationary solutions to a two-phase model with magnetic field in a half line. Nonlinear Anal: Real World Appl, 2020, 51: Art 102939
[25] Zhu L.Vanishing resistivity limit of one-dimensional two-phase model with magnetic field. J Differential Equations, 2022, 319: 211-226
[26] Zhu L, Chen Y.Global well-posedness of strong solutions to a two-phase model with magnetic field for large oscillations in three dimensions. J Differential Equations, 2019, 266: 3247-3278

THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*

THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN^*

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Cuntao xiao, Hua qiu, Zheng-an yao. THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS[J]. 数学物理学报(英文版), 2024, 44(3): 973-983.
[2]	Yuhui Chen, Qinghe Yao, Minling Li, Zheng-an Yao. GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN ${\mathbb{R}}^{3}$^*[J]. 数学物理学报(英文版), 2023, 43(3): 1301-1322.
[3]	Weixi LI, Rui XU, Tong YANG. GLOBAL WELL-POSEDNESS OF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES[J]. 数学物理学报(英文版), 2022, 42(6): 2343-2366.
[4]	Changxing MIAO, Junyong ZHANG, Jiqiang ZHENG. A NONLINEAR SCHRÖDINGER EQUATION WITH COULOMB POTENTIAL[J]. 数学物理学报(英文版), 2022, 42(6): 2230-2256.
[5]	Jinlu LI, Zhaoyang YIN, Xiaoping ZHAI. GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 2022, 42(5): 2131-2148.
[6]	晋雪婷, 肖跃龙, 于幻. GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION[J]. 数学物理学报(英文版), 2022, 42(4): 1293-1309.
[7]	陈停停, 屈爱芳, 王振. EXISTENCE AND UNIQUENESS OF THE GLOBAL L₁ SOLUTION OF THE EULER EQUATIONS FOR CHAPLYGIN GAS[J]. 数学物理学报(英文版), 2021, 41(3): 941-958.
[8]	Muhammad Zainul ABIDIN, 陈杰诚. GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES[J]. 数学物理学报(英文版), 2021, 41(1): 164-176.
[9]	苏仕斌, 赵小奎. GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2018, 38(3): 898-914.
[10]	张再云, 黄建华, 孙明保. ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R²[J]. 数学物理学报(英文版), 2017, 37(2): 385-394.
[11]	霍朝辉. GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION[J]. 数学物理学报(英文版), 2016, 36(4): 1117-1152.
[12]	夏红强. GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL HARTREE EQUATION IN HIGH DIMENSIONS[J]. 数学物理学报(英文版), 2015, 35(1): 255-274.
[13]	陈明涛. GLOBAL WELL-POSEDNESS OF THE 2D INCOMPRESSIBLE MICROPOLAR FLUID FLOWS WITH PARTIAL VISCOSITY AND ANGULAR VISCOSITY[J]. 数学物理学报(英文版), 2013, 33(4): 929-935.
[14]	蒲学科, 郭柏灵. GLOBAL WELL-POSEDNESS OF THE STOCHASTIC 2D BOUSSINESQ EQUATIONS WITH PARTIAL VISCOSITY[J]. 数学物理学报(英文版), 2011, 31(5): 1968-1984.
[15]	李用声, 杨兴雨. GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE[J]. 数学物理学报(英文版), 2011, 31(4): 1303-1317.