Regularity results for weak solutions of the 3D MHD equations

Discrete and Continuous Dynamical Systems

Volumn 10, Issue 1-2, 2004, Pages 543-556

  Wu, Jiahong ^a  

^a OKLAHOMA STATE UNIVERSITY   (United States)

Author keywords

Axisymmetry; Global regularity; MHD equations; Weak solution

Indexed keywords

EID: 2142704246     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.10.543     Document Type: Article

References (8)

1. J.T. Beale, T. Kato and A. Majda, Remarks on breakdown of smooth solutions for the 3D Euler equations, Comm. Math. Phys. 94(1984), 61-66.
2. R.E. Caflisch, I. Klapper and G. Steele, Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD, Comm. Math. Phys. 184(1997), 443-455.
3. D. Chae and J. Lee, On the regularity of axisymmetric solutions of the Navier-Stokes equations, Nonlinear Anal. 46 (2001), 727-735.
4. G. Duvaut and J.L. Lions, Inequations en thermoelasticite et magnetohydrodynamique, Ach. Rational Mech. Anal. 46(1972), 241-279.
5. M. Sermange and R. Temam, Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math. 36(1983), 635-664.
6. J. Serrin, Mathematical principles of classical mechanics, in "Handbuch der Physik", S. Flugge and C. Truesdell editors, Springer-Verlag, Berlin, 1959, 125-263.
7. J. Wu, Viscous and inviscid magneto-hydrodynamics equations, J. D'Analyse Mathématique 73 (1997), 251-265.
8. J. Wu, Analytic results related to magneto-hydrodynamic turbulence, Physica D 136 (2000), 353-372.