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Global existence and optimal decay rates of solutions for compressible Hall-MHD equations
1. | School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China, China |
References:
[1] |
M. Acheritogaray, P. Degond, A. Frouvelle and J. G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinet. Relat. Models, 4 (2011), 901-918.
doi: 10.3934/krm.2011.4.901. |
[2] |
S. A. Balbus and C. Terquem, Linear analysis of the Hall effect in protostellar disks, Astrophys. J., 552 (2001), 235-247.
doi: 10.1086/320452. |
[3] |
M. J. Benvenutti and L. C. F. Ferreira, Existence and stability of global large strong solutions for the Hall-MHD system,, preprint, ().
|
[4] |
D. Chae, P. Degond and J. G. Liu, Well-posedness for Hall-magnetohydrodynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 555-565.
doi: 10.1016/j.anihpc.2013.04.006. |
[5] |
D. Chae and J. Lee, On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256 (2014), 3835-3858.
doi: 10.1016/j.jde.2014.03.003. |
[6] |
D. Chae and M. E. Schonbek, On the temporal decay for the Hall-magnetohydrodynamic equations, J. Differential Equations, 255 (2013), 3971-3982.
doi: 10.1016/j.jde.2013.07.059. |
[7] |
Q. Chen and Z. Tan, Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations, Nonlinear Anal., 72 (2010), 4438-4451.
doi: 10.1016/j.na.2010.02.019. |
[8] |
R. J. Duan, H. X. Liu, S. J. Ukai and T. Yang, Optimal $L^p-L^q$ convergence rates for the compressible Navier-Stokes equations with potential force, J. Differential Equations, 238 (2007), 220-233.
doi: 10.1016/j.jde.2007.03.008. |
[9] |
J. S. Fan, A. Alsaedi, T. Hayat, G. Nakamura and Y. Zhou, On strong solutions to the compressible Hall-magnetohydrodynamic system, Nonlinear Anal. Real World Appl., 22 (2015), 423-434.
doi: 10.1016/j.nonrwa.2014.10.003. |
[10] |
J. S. Fan, F. C. Li and G. Nakamura, Regularity criteria for the incompressible Hall-magnetohydrodynamic equations, Nonlinear Anal., 109 (2014), 173-179.
doi: 10.1016/j.na.2014.07.003. |
[11] |
J. S. Fan and T. Ozawa, Regularity criteria for the density-dependent Hall-magnetohydrodynamics, Appl. Math. Lett., 36 (2014), 14-18.
doi: 10.1016/j.aml.2014.04.010. |
[12] |
J. S. Fan, S. X. Huang and G. Nakamura, Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations, Appl. Math. Lett., 26 (2013), 963-967.
doi: 10.1016/j.aml.2013.04.008. |
[13] |
T. G. Forbes, Magnetic reconnection in solar flares, Geophys. Astrophys. Fluid Dyn., 62 (1991), 15-36.
doi: 10.1080/03091929108229123. |
[14] |
J. C. Gao, Q. Tao and Z. A. Yao, Long-time behavior of solution for the compressible nematic liquid crystal flows in $\mathbbR^3$,, preprint, ().
|
[15] |
J. C. Gao, Y. H. Chen and Z. A. Yao, Long-time behavior of solution to the compressible magnetohydrodynamic equations, Nonlinear Anal., 128 (2015), 122-135.
doi: 10.1016/j.na.2015.07.028. |
[16] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[17] |
H. Homann and R. Grauer, Bifurcation analysis of magnetic reconnection in Hall-MHD systems, Phys. D, 208 (2005), 59-72.
doi: 10.1016/j.physd.2005.06.003. |
[18] |
X. P. Hu and G. C. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833.
doi: 10.1137/120892350. |
[19] |
F. C. Li and H. J. Yu, Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations, Proc. Roy. Soc. Edinburgh Sect. A, 141 (2011), 109-126.
doi: 10.1017/S0308210509001632. |
[20] |
A. Matsumura and T. Nishida, The initial value problems for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[21] |
P. D. Mininni, D. O. Gòmez and S. M. Mahajan, Dynamo action in magnetohydrodynamics and Hall magnetohydrodynamics, Astrophys. J., 587 (2003), 472-481.
doi: 10.1086/368181. |
[22] |
L. Nirenberg, On elliptic partial differential euations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[23] |
M. E. Schonbek, $L^2$ decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 88 (1985), 209-222.
doi: 10.1007/BF00752111. |
[24] |
D. A. Shalybkov and V. A. Urpin, The Hall effect and the decay of magnetic fields, Astron. Astrophys., (1997), 685-690. |
[25] |
Z. Tan and H. Q. Wang, Optimal decay rates of the compressible magnetohydrodynamic equations, Nonlinear Anal. Real World Appl., 14 (2013), 188-201.
doi: 10.1016/j.nonrwa.2012.05.012. |
[26] |
Y. J. Wang and Z. Tan, Global existence and optimal decay rate for the strong solutions in $H^2$ to the compressible Navier-Stokes equations, Appl. Math. Lett., 24 (2011), 1778-1784.
doi: 10.1016/j.aml.2011.04.028. |
[27] |
W. J. Wang and W. K. Wang, Decay rates of the compressible Navier-Stokes-Korteweg equations with potential forces, Discrete Contin. Dyn. Syst., 35 (2015), 513-536.
doi: 10.3934/dcds.2015.35.513. |
[28] |
W. J. Wang, Large time behavior of solutions to the compressible Navier-Stokes equations with potential force, J. Math. Anal. Appl., 423 (2015), 1448-1468.
doi: 10.1016/j.jmaa.2014.10.050. |
[29] |
M. Wardle, Star formation and the Hall effect, Astrophys. Space Sci., 292 (2004), 317-323. |
[30] |
S. K. Weng, On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system,, preprint, ().
|
show all references
References:
[1] |
M. Acheritogaray, P. Degond, A. Frouvelle and J. G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinet. Relat. Models, 4 (2011), 901-918.
doi: 10.3934/krm.2011.4.901. |
[2] |
S. A. Balbus and C. Terquem, Linear analysis of the Hall effect in protostellar disks, Astrophys. J., 552 (2001), 235-247.
doi: 10.1086/320452. |
[3] |
M. J. Benvenutti and L. C. F. Ferreira, Existence and stability of global large strong solutions for the Hall-MHD system,, preprint, ().
|
[4] |
D. Chae, P. Degond and J. G. Liu, Well-posedness for Hall-magnetohydrodynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 555-565.
doi: 10.1016/j.anihpc.2013.04.006. |
[5] |
D. Chae and J. Lee, On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256 (2014), 3835-3858.
doi: 10.1016/j.jde.2014.03.003. |
[6] |
D. Chae and M. E. Schonbek, On the temporal decay for the Hall-magnetohydrodynamic equations, J. Differential Equations, 255 (2013), 3971-3982.
doi: 10.1016/j.jde.2013.07.059. |
[7] |
Q. Chen and Z. Tan, Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations, Nonlinear Anal., 72 (2010), 4438-4451.
doi: 10.1016/j.na.2010.02.019. |
[8] |
R. J. Duan, H. X. Liu, S. J. Ukai and T. Yang, Optimal $L^p-L^q$ convergence rates for the compressible Navier-Stokes equations with potential force, J. Differential Equations, 238 (2007), 220-233.
doi: 10.1016/j.jde.2007.03.008. |
[9] |
J. S. Fan, A. Alsaedi, T. Hayat, G. Nakamura and Y. Zhou, On strong solutions to the compressible Hall-magnetohydrodynamic system, Nonlinear Anal. Real World Appl., 22 (2015), 423-434.
doi: 10.1016/j.nonrwa.2014.10.003. |
[10] |
J. S. Fan, F. C. Li and G. Nakamura, Regularity criteria for the incompressible Hall-magnetohydrodynamic equations, Nonlinear Anal., 109 (2014), 173-179.
doi: 10.1016/j.na.2014.07.003. |
[11] |
J. S. Fan and T. Ozawa, Regularity criteria for the density-dependent Hall-magnetohydrodynamics, Appl. Math. Lett., 36 (2014), 14-18.
doi: 10.1016/j.aml.2014.04.010. |
[12] |
J. S. Fan, S. X. Huang and G. Nakamura, Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations, Appl. Math. Lett., 26 (2013), 963-967.
doi: 10.1016/j.aml.2013.04.008. |
[13] |
T. G. Forbes, Magnetic reconnection in solar flares, Geophys. Astrophys. Fluid Dyn., 62 (1991), 15-36.
doi: 10.1080/03091929108229123. |
[14] |
J. C. Gao, Q. Tao and Z. A. Yao, Long-time behavior of solution for the compressible nematic liquid crystal flows in $\mathbbR^3$,, preprint, ().
|
[15] |
J. C. Gao, Y. H. Chen and Z. A. Yao, Long-time behavior of solution to the compressible magnetohydrodynamic equations, Nonlinear Anal., 128 (2015), 122-135.
doi: 10.1016/j.na.2015.07.028. |
[16] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[17] |
H. Homann and R. Grauer, Bifurcation analysis of magnetic reconnection in Hall-MHD systems, Phys. D, 208 (2005), 59-72.
doi: 10.1016/j.physd.2005.06.003. |
[18] |
X. P. Hu and G. C. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833.
doi: 10.1137/120892350. |
[19] |
F. C. Li and H. J. Yu, Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations, Proc. Roy. Soc. Edinburgh Sect. A, 141 (2011), 109-126.
doi: 10.1017/S0308210509001632. |
[20] |
A. Matsumura and T. Nishida, The initial value problems for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[21] |
P. D. Mininni, D. O. Gòmez and S. M. Mahajan, Dynamo action in magnetohydrodynamics and Hall magnetohydrodynamics, Astrophys. J., 587 (2003), 472-481.
doi: 10.1086/368181. |
[22] |
L. Nirenberg, On elliptic partial differential euations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[23] |
M. E. Schonbek, $L^2$ decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 88 (1985), 209-222.
doi: 10.1007/BF00752111. |
[24] |
D. A. Shalybkov and V. A. Urpin, The Hall effect and the decay of magnetic fields, Astron. Astrophys., (1997), 685-690. |
[25] |
Z. Tan and H. Q. Wang, Optimal decay rates of the compressible magnetohydrodynamic equations, Nonlinear Anal. Real World Appl., 14 (2013), 188-201.
doi: 10.1016/j.nonrwa.2012.05.012. |
[26] |
Y. J. Wang and Z. Tan, Global existence and optimal decay rate for the strong solutions in $H^2$ to the compressible Navier-Stokes equations, Appl. Math. Lett., 24 (2011), 1778-1784.
doi: 10.1016/j.aml.2011.04.028. |
[27] |
W. J. Wang and W. K. Wang, Decay rates of the compressible Navier-Stokes-Korteweg equations with potential forces, Discrete Contin. Dyn. Syst., 35 (2015), 513-536.
doi: 10.3934/dcds.2015.35.513. |
[28] |
W. J. Wang, Large time behavior of solutions to the compressible Navier-Stokes equations with potential force, J. Math. Anal. Appl., 423 (2015), 1448-1468.
doi: 10.1016/j.jmaa.2014.10.050. |
[29] |
M. Wardle, Star formation and the Hall effect, Astrophys. Space Sci., 292 (2004), 317-323. |
[30] |
S. K. Weng, On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system,, preprint, ().
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