A Class Of The Combustion Non-Newtonian Fluids With Vacuum

In nature,all things obey the invariable order of nature,for instance, conservation laws (mass, momentum and energy),universal gravitation etc.We are opening out,conquering and transforming the nature by these foundational laws, Of course,it is out of question that the flowing gas or liquid (fluid)obey the order of nature.for example, the fluids obey conver-sation lows of mass and momentum.If we want to know the state of fluids.we may solve equations that are constructed by these conversation laws. With the development of the tech-nology.the reaction of the fluids follows some law in the process of product and nature.The classical reaction fluid is the combustion of the gas flow, this reaction widely exists in na-ture,it is necessary to studying these dynamics equations system.In this paper, we mainly study two class of compressible non-Newtonian fluid models. First of all, we discuss the following model in one space dimensional bounded interval with following initial-boundary value: whereρ, uandzdenote the unknown density,velocity and the per centum of the responseless gas in the gas flow.respectively.ΩT=I×(0, T), I=(0,1).In this paper,we studv local existence and uniqueness of solutions to the initial bound- ary value problem (0.0.16)-(0.0.17)with nonnegative initial densities.Now we can state our main results in this paper.定理0.4. Assume that 4/30 s∈R,γ>1 andρ0,z0is Smooth,u0∈H01(I)∩H2(I) is the solution of the following problem When we estimate the approximate solution,we need to estimate|u(xx)k|L2(I).And finally we obtain:C only depends onM0,M0= 1+|ρ0|H1(I)+|z0|H1(I)+|g|L2(I)+|A|W1,∞(R)+|K|W1.∞(R). Using(0.0.27),we could take limits with respect to k and get following theorem. 定理0.5.Assume thntρ0≥δ>0 is sufficiently smooth,whereδisαgiven constant. 4/32,μ0>0.Similar as the previous part,for above system,we also can prove定理0.6.Assume that p>2,0≤ρ0,0