The Study On The Well-Posedness Of The Compressible Two-Fluid Model

Two-fluid model exists widely in industrial processes such as energy power,aerospace,biomedicine,petrochemicals,and food processing.Two-fluid mechanics is an important theoretical basis in modern industry and plays an important role in guiding and developing modern industries.In the study of the two-fluid model,some results are obtained depending on the domination condition(n0≤c0ρ0 or ρ0≤c1n0,where n0 and ρ0 represent the initial densities of the two fluids respectively,c0 and c1 are some positive constants),but the case without any domination condition makes the two-fluid model more realistic in some physical situations and more "two fluids" properties from mathematical points of view.In the absence of domination conditions,there are no results on the well-posedness to the Cauchy problem of the one-dimensional two-fluid Navier-Stokes equations.Based on this,the paper is planning to study this issuer.We consider the Cauchy problem to the compressible two-fluid Navier-Stokes equations in one-dimensional space allowing vacuum.By constructing a priori estimates and using weighted energy estimates to overcome the non-integrable property of density itself,it is shown that the compressible two-fluid Navier-Stokes equations admit global strong solution with the large initial value.Note that this result is proved without smallness condition on the initial value.