Study On The Well - Posedness And Blasting Of Non - Newtonian

In this paper, under different conditions, we discuss the strong solution and smooth solution to compressible non-Newtonian fluids in 1-dimensional and 3-dimensional spaces separately, and we get the following results:●The initial-boundary problem of a class of non-Newtonian fluid with vac-uum, singularity and density-dependent viscosity. By regularizing the singularity term and constructing the approximate solutions, we prove the local posedness of strong solution to the initial boundary problem. Under the methods of energy estimates and Sobolev embedding theorem, we derive a blowup criterion for the strong solution with certain initial profiles.● The blow-up of smooth solution to the initial problem for a compressible non-Newtonian fluid with compact density. Without taking into account of heat phenomena, we prove that there exists no global in time smooth solutions to the initial problem if the total mass and momentum of the system are conserved.