Strong solutions to compressible–incompressible two-phase flows with phase transitions. (August 2020)

• Record Type: Journal Article
• Authors: Watanabe, Keiichi
• Is Part Of: Nonlinear analysis. Volume 54(2020)
• Publication Date: 2020-08
• Subjects: Free boundary problem -- Phase transition -- Two-phase problem -- Maximal regularity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103101
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We 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 L p − L q regularity class provided the initial data are small in their natural norms.