On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface

In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform Wq2−1/q domain in RN (N≥2). We prove the local in the time unique existence theorem for our problem in the Lp in time and Lq in space framework with 2

Keywords:

• Multiplier (Fourier analysis)
• Navier–Stokes equations
• Analytic semigroup
• Fourier transform
• Existence theorem
• Stokes operator
• Mathematical analysis
• Contraction mapping
• Mathematics
• Domain (mathematical analysis)

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