December  2016, 9(6): 2113-2127. doi: 10.3934/dcdss.2016087

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

1. 

School of Mathematics, Center for Nonlinear Studies, Northwest University, Xi'an 71006901, China

2. 

Department of Mathematics, Yunnan Nationalities University, Kunming 650031, China

Received  July 2015 Revised  September 2016 Published  November 2016

The purpose of this paper is to build the existence of time-spatial global regular solution to the coupled Navier-Stokes and Maxwell equations.
Citation: Wenjing Song, Ganshan Yang. The regularization of solution for the coupled Navier-Stokes and Maxwell equations. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2113-2127. doi: 10.3934/dcdss.2016087
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, 272 (1972), 47. doi: 10.1098/rsta.1972.0032. Google Scholar

[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. doi: 10.1007/s00021-004-0107-9. Google Scholar

[3]

A. Kiselev and O. Ladyzhenskaya, On existence and unieness of solutions of nonstationary problem for viscous incompressible fluid,, Izv. Akad. Nauk SSSR, 21 (1957), 655. Google Scholar

[4]

A. Kulikovskiy and G. Lyubimov, Magnetohydrodynamics,, Addison-Wesley, (1965). Google Scholar

[5]

O. Ladyzhenskaya and V. Solonnikov, Solution of some nonstationary magnetohydrodynamical problems for incompressible fluid,, Trudy of steklov Math. Inst., 69 (1960), 115. Google Scholar

[6]

O. Ladyzhenskaya, Modfications of the Navier-Stokes equations forlarge velocity gradients,, Zap. Nauchn. Semin. LOMI, 7 (1968), 126. Google Scholar

[7]

O. Lehto, Proceedings of the International Congress of Mathematicians Hesinkin,, Academia Scientiarum Fennica, (1980). Google Scholar

[8]

O. Ladyzhenskaya, Boundary-valeu Problem of Mathematical Physics,, Nauka, (1973). Google Scholar

[9]

R. Moreau, Magnetohydrodynamics,, Kluwer, (1990). doi: 10.1007/978-94-015-7883-7. Google Scholar

show all references

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, 272 (1972), 47. doi: 10.1098/rsta.1972.0032. Google Scholar

[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. doi: 10.1007/s00021-004-0107-9. Google Scholar

[3]

A. Kiselev and O. Ladyzhenskaya, On existence and unieness of solutions of nonstationary problem for viscous incompressible fluid,, Izv. Akad. Nauk SSSR, 21 (1957), 655. Google Scholar

[4]

A. Kulikovskiy and G. Lyubimov, Magnetohydrodynamics,, Addison-Wesley, (1965). Google Scholar

[5]

O. Ladyzhenskaya and V. Solonnikov, Solution of some nonstationary magnetohydrodynamical problems for incompressible fluid,, Trudy of steklov Math. Inst., 69 (1960), 115. Google Scholar

[6]

O. Ladyzhenskaya, Modfications of the Navier-Stokes equations forlarge velocity gradients,, Zap. Nauchn. Semin. LOMI, 7 (1968), 126. Google Scholar

[7]

O. Lehto, Proceedings of the International Congress of Mathematicians Hesinkin,, Academia Scientiarum Fennica, (1980). Google Scholar

[8]

O. Ladyzhenskaya, Boundary-valeu Problem of Mathematical Physics,, Nauka, (1973). Google Scholar

[9]

R. Moreau, Magnetohydrodynamics,, Kluwer, (1990). doi: 10.1007/978-94-015-7883-7. Google Scholar

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