[1] Cannone M, Chen Q, Miao C. A losing estimate for the ideal MHD equations with application to blow-up criterion. SIAM J Math Anal, 2007, 38(6):1847-1859
[2] Caflisch R E, Klapper I, Steele G. Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD. Comm Math Phys, 1997, 184(2):443-455
[3] Du Y, Liu Y, Yao Z. Remarks on the blow-up criteria for three-dimensional ideal magnetohydrodynamics equations. J Math Phys, 2009, 50(2):023507, 8 pp
[4] Ferrari A B. On the blow-up of solutions of 3-D Euler equations in a bounded domain. Comm Math Phys, 1993, 155(2):277-294
[5] Hartman Ph. Ordinary Differential Equations. 2nd ed. Boston, Basel, Stuttgart:Birkhäuser, 1982
[6] Hu X, Hynd R. A blowup criterion for ideal viscoelastic flow. J Math Fluid Mech, 2013, 15(3):431-437
[7] Kato T. Nonstationary flows of viscous and ideal fluids in R3. J Funct Anal, 1972, 9:296-305
[8] Gurtin M E. An Introduction to Continuum Mechanics, Mathematics in Science and Enineering. Vol 158. New York:Academic Press, 1981
[9] Larson R G. The Structure and Rheology of Complex Fluids. New York:Oxford University Press, 1995
[10] Majda A. Compressible fluid flow and systems of conservation laws in several space variables. New York:Springer, 1984
[11] Mahalov A, Nicolaenko B, Golse F. Non blow-up of the 3D ideal magnetohydrodynamics equations for a class of three-dimensional initial data in cylindrical domains. Zap Nauchn Sem S -Peterburg Otdel Mat Inst Steklov (POMI), 2004, 318:203-219; translation in J Math Sci (NY), 2006, 136(2):3768-3777
[12] Ogawa T, Taniuchi Y. On blow-up criteria of smooth solutions to the 3D Euler equations in a bounded domain. J Differential Equations, 2003, 190(1):39-63
[13] Temam R. On the Euler equations of incompressible perfect fluids. J Funct Anal, 1975, 20(1):32-43
[14] Vishik M. Incompressible flows of an ideal fluid with unbounded vorticity. Comm Math Phys, 2000, 213(3):697-731
[15] Zhang Z-F, Liu X-F. On the blow-up criterion of smooth solutions to the 3D ideal MHD equations. Acta Math Appl Sin, Engl Ser, 2004, 20(4):695-700
[16] Zhu L, Wang F. A new blowup criterion for ideal viscoelastic flow. J Partial Differ Equ, 2015, 28(1):23-29 |