On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations

Beale, J.T., Kato, T., Majda, A.J. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys., 94: 61–66 (1984)

Bergh, J., Löfstrom, J. Interpolation spaces, An Introduction. Springer-Verlag, New York, 1976

Caflisch, R.E., I. Klapper, I., Steele, G. Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD. Comm. Math. Phys., 184: 443–455 (1997)

Frazier, M., Torres, R., Weiss, G. The boundedness of Caldern-Zygmund operators on the spaces $$ \ifmmode\expandafter\dot\else\expandafter\.\fi{F}^{{\alpha ,q}}_{p} . $$ Rev. Mat. Iberoamericana 4: 41–72 (1988)

Kozono, H., Ogawa, T., Taniuchi, Y. The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. Math. Z., 242: 251–278 (2002)

Majda, A.J. Compressible fluid flow and systems of conservation laws in several space variables. Applied Mathematical Sciences, 53, Springer-Verlag, New York, 1984

Majda, A.J. Bertozzi, A.L. Vorticity and incompressible flow. Cambridge Texts in Applied Mathematics, 27, Cambridge University Press, Cambridge, 2002

Stein, E.M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton University Press, Princeton, 1993

Tribel, H. Theory of Function Spaces. Monograph in mathematics, Vol.78 , Birkhauser Verlag, Basel, 1983