ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES

In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3 D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations.First,it is shown that there exists a positive constant ε such that the solution(ρ,u,θ) to the full compressible Navier-Stokes equations can be extended beyond t=T provided that one of the following two conditions holds:■To the best of our knowledge,this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid.Second,we establish some blow-up criteria in anisotropic Lebesgue spaces for the finite blow-up time T~*:■Third,without the condition on p in(0.1) and(0.3),the results also hold for the 3 D nonhomogeneous incompressible Navier-Stokes equations.The appearance of a vacuum in these systems could be allowed.