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| 1 | Global fast and slow solutions of a localized problem with free boundary显示文摘In this paper,we consider a localized problem with free boundary for the heat equation in higher space dimensions and heterogeneous environment.For simplicity,we assume that the environment and solution are radially symmetric.First,by using the contraction mapping theorem,we prove that the local solution exists and is unique.Then,some sufficient conditions are given under which the solution will blow up in finite time.Our results indicate that the blowup occurs if the initial data are sufficiently large.Finally,the long time behavior of the global solution is discussed.It is shown that the global fast solution does exist if the initial data are sufficiently small,while the global slow solution is possible if the initial data are suitably large. | ZHOU Peng LIN ZhiGui | 2012 | Science China Mathematics2012，55，9： | 3 |
| 2 | Blowup mechanism for viscous compressible heat-conductive magnetohydrodynamic flows in three dimensions显示文摘We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic(MHD)system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale-Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al.(2011). The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows,which extend the results established by Fan et al.(2010), and Huang and Li(2009). In addition, the viscous coefficients are only restricted by the physical conditions in this paper. | WANG YongFu DU LiLi LI Shan | 2015 | Science China Mathematics2015，58，8： | 1 |
| 3 | Blow-up Criterion for Three-dimensional Compressible Viscoelastic Fluids with Vacuum显示文摘In this paper, we study a Cauchy problem for the equations of 3D compressible viscoelastic fluids with vacuum. We establish a blow-up criterion for the local strong solutions in terms of the upper bound of the density and deformation gradient. | Sheng Quan LIU Jun Ning ZHAO | 2013 | Acta Mathematica Sinica,English Series2013，29，6： | 0 |
| 4 | Global Well-Posedness of Classical Solutions with Large Initial Data to the Two-Dimensional Isentropic Compressible Navier-Stokes Equations显示文摘 | ZHANG Peixin DENG Xuemei ZHAO Junning | 2014 | Journal of Partial Differential Equations2014，27，2： | 0 |
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