Abstract
We prove the existence and uniqueness of global strong solutions to the Maxwell–Navier–Stokes system in a two dimensional bounded domain with Navier-type boundary condition for the velocity.
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D’Ambrosio, D., Giordano, D.: Electromagnetic fluid dynamics for aerospace applications. Part I: classification and critical review of physical models. In: Proceedings of the 35th AIAA Plasmadynamics and Lasers Conference, Portland, Ore, USA, June 2004, AIAA Paper 2004–2165
D’Ambrosio, D., Pandol, M., Giordano, D.: Electromagnetic fluid dynamics for aerospace applications. Part II: numerical simulations using different physical models. In: Proceedings of the 35th AIAA Plasma Dynamics and Lasers Conference, Portland, Ore, USA, June 2004, AIAA Paper 2004–2362
Davidson, P.A.: An Introduction to Magnetohydrodynamics. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2001)
Masmoudi, N.: Global well posedness for the Maxwell–Navier–Stokes system in 2D. J. Math. Pures Appl. 93, 559–571 (2010)
Kang, E., Lee, J.: Notes on the global well-posedness for the Maxwell–Navier–Stokes system. Abstr. Appl. Anal. 6(2013) Art. ID 402793
Duan, R.: Green’s function and large time behavior of the Navier–Stokes–Maxwell system. Anal. Appl. 10(2), 133–197 (2012)
Fan, J., Zhou, Y.: Regularity criteria for the 3D density-dependent incompressible Maxwell–Navier–Stokes system. Comput. Math. Appl. 73, 2421–2425 (2017)
Brezis, H., Gallouet, T.: Nonlinear Schrödinger evolution equations. Nonlinear Anal. 4(4), 677–681 (1980)
Bourguignon, J., Brezis, H.: Remarks on the Euler equation. J. Funct. Anal. 15, 341–363 (1974)
Xiao, Y., Xin, Z.: On the vanishing viscosity limit for the 3D Navier–Stokes equations with a slip boundary condition. Commun. Pure Appl. Math. 60, 1027–1055 (2007)
Lions, P.L.: Mathematical Topics in Fluid Mechanics. Compressible Models, vol. 2. Oxford University Press, New York (1998)
Acknowledgements
This paper is partially supported by NSFC (No. 11971234). The authors are indebted to the referees for their careful reading of the manuscript.
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Fan, J., Ozawa, T. Global solutions to the Maxwell–Navier–Stokes system in a bounded domain in 2D. Z. Angew. Math. Phys. 71, 136 (2020). https://doi.org/10.1007/s00033-020-01364-y
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DOI: https://doi.org/10.1007/s00033-020-01364-y