On the Free Boundary Problem of Three-dimensional Compressible Euler Equations in Physical Vacuum
نویسنده
چکیده
In this paper, we establish a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, the γ-gas law equation of state for γ = 2 and the general initial density ρ0 ∈ H6(Ω). Because of the degeneracy of the initial density, we investigate the estimates of the horizontal spatial and time derivatives and then obtain the estimates of the normal or full derivatives through the elliptic-type estimates. We derive a mixed space-time interpolation inequality which play a vital role in our energy estimates. The results improve the known results (Comm. Math. Phys. 296 (2010) 559-587) on a priori estimates for the case γ = 2. CONTENTS
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تاریخ انتشار 2013