The Blow-up Criterion Of Strong Solution With Periodic Problem To The Simplified Liquid-Gas Two-Phase Flow Model

In this paper,we establish a new blow-up criterion for the strong solutions to the 3D simplified viscous liquid-gas two phase flow model with the periodic boundary condition,which is controlled by the norm L∞(0,T;L3(Ω))of the velocity divergence and the L∞(0,T;Lβ(Ω)),β∈(1,∞)of the liquid mass.There is no additional restriction on the viscosity coefficient.In Chapter 1,we introduce some related backgrounds about the well-posedness of solutions and large time behavior of solutions to the liquid-gas two-phase flow model;In Chapter 2,firstly,we obtain the existence of local strong solution to the liquid-gas two-phase flow model,secondly,by contradiction,we shall as-sume that(?)(‖m‖β+‖ divu ‖3)<∞,where 0<T<T*,without the assumption of 25/3μ>λ,we proved(?)‖m‖∞<∞,lastly,we extend the solution,which implies that T*should not be the maximal existence time of strong solution,then we get the contradiction.In Chapter 3,in the Appendix,we give some basic results.