# American Institute of Mathematical Sciences

2013, 2013(special): 207-216. doi: 10.3934/proc.2013.2013.207

## An approximation model for the density-dependent magnetohydrodynamic equations

 1 Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037 2 Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received  July 2012 Published  November 2013

The global Cauchy problem for an approximation model for the density-dependent MHD system is studied. The vanishing limit on $\alpha$ is also discussed.
Citation: Jishan Fan, Tohru Ozawa. An approximation model for the density-dependent magnetohydrodynamic equations. Conference Publications, 2013, 2013 (special) : 207-216. doi: 10.3934/proc.2013.2013.207
##### References:
 [1] H. Abidi, M. Paicu, Global existence for the MHD system in critical spaces,, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 447.   Google Scholar [2] B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics,, Differential and Integral Equations, 11 (1998), 377.   Google Scholar [3] J. Fan, T. Ozawa, Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model,, Kinetic Related Models 2 (2009), 2 (2009), 293.   Google Scholar [4] J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation,, Adv. Differential Equations, 2 (1997), 427.   Google Scholar [5] M. Holst, E. Lunasin, G. Tsogtgerel, Analysis of a general family of regularized Navier-Stokes and MHD models,, J. of Nonlinear Science, 20 (2010), 523.   Google Scholar [6] J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models,, J. Math. Phys., 48 (2007).   Google Scholar [7] Y. Yu, K.Li, Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations,, J. Math. Anal. Appl., 329 (2007), 298.   Google Scholar [8] Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms,, preprint, (2009).   Google Scholar [9] Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations,, Math. Meth. Appl. Sci. 33 (2010), 33 (2010), 1350.   Google Scholar

show all references

##### References:
 [1] H. Abidi, M. Paicu, Global existence for the MHD system in critical spaces,, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 447.   Google Scholar [2] B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics,, Differential and Integral Equations, 11 (1998), 377.   Google Scholar [3] J. Fan, T. Ozawa, Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model,, Kinetic Related Models 2 (2009), 2 (2009), 293.   Google Scholar [4] J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation,, Adv. Differential Equations, 2 (1997), 427.   Google Scholar [5] M. Holst, E. Lunasin, G. Tsogtgerel, Analysis of a general family of regularized Navier-Stokes and MHD models,, J. of Nonlinear Science, 20 (2010), 523.   Google Scholar [6] J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models,, J. Math. Phys., 48 (2007).   Google Scholar [7] Y. Yu, K.Li, Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations,, J. Math. Anal. Appl., 329 (2007), 298.   Google Scholar [8] Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms,, preprint, (2009).   Google Scholar [9] Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations,, Math. Meth. Appl. Sci. 33 (2010), 33 (2010), 1350.   Google Scholar
 [1] Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637 [2] Guillermo Reyes, Juan-Luis Vázquez. Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Communications on Pure & Applied Analysis, 2009, 8 (2) : 493-508. doi: 10.3934/cpaa.2009.8.493 [3] Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709 [4] Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$-rule. Inverse Problems & Imaging, 2012, 6 (1) : 133-146. doi: 10.3934/ipi.2012.6.133 [5] Arunima Bhattacharya, Micah Warren. $C^{2, \alpha}$ estimates for solutions to almost Linear elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021024 [6] Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247 [7] Yunfei Lv, Rong Yuan, Yuan He. Wavefronts of a stage structured model with state--dependent delay. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4931-4954. doi: 10.3934/dcds.2015.35.4931 [8] Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1779-1799. doi: 10.3934/dcdss.2020454 [9] Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$\alpha$ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 [10] Wen-Bin Yang, Yan-Ling Li, Jianhua Wu, Hai-Xia Li. Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2269-2290. doi: 10.3934/dcdsb.2015.20.2269 [11] Irena PawŃow, Wojciech M. Zajączkowski. Global regular solutions to three-dimensional thermo-visco-elasticity with nonlinear temperature-dependent specific heat. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1331-1372. doi: 10.3934/cpaa.2017065 [12] Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 [13] Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521

Impact Factor:

## Metrics

• HTML views (0)
• Cited by (0)

• on AIMS