Abstract
This paper proves a regularity criterion for the \(3D\) full compressible Navier-Stokes-Maxwell system in a bounded domain.
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Acquistapace, P.: On \(\mathit{BMO}\) regularity for linear elliptic systems. Ann. Mat. Pura Appl. 161, 231–269 (1992)
Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Commun. Pure Appl. Math. 12, 623–727 (1959)
Brézis, H., Wainger, S.: A note on limiting cases of Sobolev embeddings and convolution inequalities. Commun. Partial Differ. Equ. 5, 773–789 (1980)
Cho, Y., Kim, H.: Existence results for viscous polytropic fluids with vacuum. J. Differ. Equ. 228, 377–411 (2006)
Fan, J., Jiang, S., Ou, Y.: A blow-up criterion for the compressible viscous heat-conductive flows. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 27, 337–350 (2010)
Fan, J., Li, F., Nakamura, G.: Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bounded domain. Z. Angew. Math. Phys. 66, 1581–1593 (2015)
Fan, J., Li, F., Nakamura, G.: Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain. Kinet. Relat. Models 9, 443–453 (2016)
Hoff, D.: Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data. J. Differ. Equ. 120, 215–254 (1995)
Hoff, D.: Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat-conducting fluids. Arch. Ration. Mech. Anal. 139, 303–354 (1997)
Huang, X., Li, J.: Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows. Commun. Math. Phys. 324, 147–171 (2013)
Imai, I.: General principles of magneto-fluid dynamics. In: Yukawa, H. (ed.) Magneto-Fluid Dynamics. Suppl. Prog. Theor. Phys., vol. 24, pp. 1–34. RIFP Kyoto Univ., Kyoto (1962)
Jiang, S., Li, F.C.: Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations. Asymptot. Anal. 95, 161–185 (2015)
Jiang, S., Li, F.C.: Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system. Sci. China Math. 58, 61–76 (2015)
Kawashima, S., Shizuta, Y.: Magnetohydrodynamic approximation of the complete equations for an eletromagnetic fluid. Tsukuba J. Math. 10(1), 131–149 (1986)
Kawashima, S., Shizuta, Y.: Magnetohydrodynamic approximation of the complete equations for an eletromagnetic fluid II. Proc. Jpn. Acad., Ser. A, Math. Sci. 62, 181–184 (1986)
Li, F.C., Mu, Y.: Low Mach number limit of the full compressible Navier-Stokes-Maxwell system. J. Math. Anal. Appl. 412(1), 334–344 (2014)
Sun, Y., Wang, C., Zhang, Z.: A Beale-Kato-Majda criterion for three dimensional compressible viscous heat-conductive flows. Arch. Ration. Mech. Anal. 201, 727–742 (2011)
Sun, Y., Wang, C., Zhang, Z.: A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations. J. Math. Pures Appl. 95, 36–47 (2011)
Wen, H., Zhu, C.: Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum. Adv. Math. 248, 534–572 (2013)
Acknowledgements
Fan is supported by NSFC (Grant No. 11171154). Li is supported partially by NSFC (Grant Nos. 11271184, 11671193) and PAPD.
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Fan, J., Li, F. & Nakamura, G. A Regularity Criterion for the \(3D\) Full Compressible Navier-Stokes-Maxwell System in a Bounded Domain. Acta Appl Math 149, 1–10 (2017). https://doi.org/10.1007/s10440-016-0085-y
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DOI: https://doi.org/10.1007/s10440-016-0085-y