Strong solutions to compressible–incompressible two-phase flows with phase transitions

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Keiichi WatanabeAbstractWe consider a free boundary problem of compressible–incompressible two-phase flows with phase transitions in general domains of N-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier–Stokes–Korteweg equations and the Navier–Stokes equations, respectively. This paper shows that for given T>0 the problem admits a unique strong solution on (0,T) in the maximal Lp−Lq regularity class provided the initial data are small in their natural norms.

Source: Nonlinear Analysis: Real World Applications - January 24, 2020 Category: Research Source Type: research