The regularization of solution for the coupled Navier-Stokes and Maxwell equations

Wenjing  Song; Ganshan  Yang

doi:10.3934/dcdss.2016087

Article Contents

2016, Volume 9, Issue 6: 2113-2127. Doi: 10.3934/dcdss.2016087

This issue Previous Article Quasineutral limit of the Euler-Poisson system under strong magnetic fields Next Article Global exact controllability and asympotic stabilization of the periodic two-component $\mu\rho$-Hunter-Saxton system

The regularization of solution for the coupled Navier-Stokes and Maxwell equations

Wenjing Song^1, and
Ganshan Yang^2,

1.
School of Mathematics, Center for Nonlinear Studies, Northwest University, Xi'an 71006901
2.
Department of Mathematics, Yunnan Nationalities University, Kunming 650031

Received: June 30, 2015

Revised: August 31, 2016

Published: November 2016

Abstract Related Papers Cited by

Abstract

The purpose of this paper is to build the existence of time-spatial global regular solution to the coupled Navier-Stokes and Maxwell equations.

Keywords:

Mathematics Subject Classification: 35Q35, 49N60.

Citation:

Related Papers

Cited by

References

[1]	T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 272 (1972), 47-78.doi: 10.1098/rsta.1972.0032.
[2]	M. D. Gunzburger, O. A. Ladyzhenskaya and J. S. Peterson, On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equation, Journal of Mathematical Fluid Mechanics, 6 (2004), 462-468.doi: 10.1007/s00021-004-0107-9.
[3]	A. Kiselev and O. Ladyzhenskaya, On existence and unieness of solutions of nonstationary problem for viscous incompressible fluid, Izv. Akad. Nauk SSSR, Ser. Math., 21 (1957), 655-680.
[4]	A. Kulikovskiy and G. Lyubimov, Magnetohydrodynamics, Addison-Wesley, Resding, 1965.
[5]	O. Ladyzhenskaya and V. Solonnikov, Solution of some nonstationary magnetohydrodynamical problems for incompressible fluid, Trudy of steklov Math. Inst., 69 (1960), 115-173.
[6]	O. Ladyzhenskaya, Modfications of the Navier-Stokes equations forlarge velocity gradients, Zap. Nauchn. Semin. LOMI, 7 (1968), 126-154.
[7]	O. Lehto, Proceedings of the International Congress of Mathematicians Hesinkin, Academia Scientiarum Fennica, 1980.
[8]	O. Ladyzhenskaya, Boundary-valeu Problem of Mathematical Physics, Nauka, moscow, 1973; Springer, New York, 1985(English translation).
[9]	R. Moreau, Magnetohydrodynamics, Kluwer, Dorcdrecht, 1990.doi: 10.1007/978-94-015-7883-7.