Local Solvability for a Compressible Fluid Model of Korteweg Type on General Domains

Suma Inna and Hirokazu Saito ()
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Suma Inna: Mathematics Department, Faculty of Science and Technology, Universitas Islam Negeri Syarif Hidayatullah Jakarta, Jl. Ir. H. Juanda No. 95, Ciputat 15412, Indonesia
Hirokazu Saito: Graduate School of Informatics and Engineering, The University of Electro-Communications, 5-1 Chofugaoka 1-chome, Chofu, Tokyo 182-8585, Japan

Mathematics, 2023, vol. 11, issue 10, 1-41

Abstract: In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N -dimensional Euclidean space for N ≥ 2 . The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In the Korteweg-type model, the stress tensor is given by the sum of the standard viscous stress tensor and the so-called Korteweg stress tensor, including higher order derivatives of the fluid density. The local existence of strong solutions is proved in an L p -in-time and L q -in-space setting, p ∈ ( 1 , ∞ ) and q ∈ ( N , ∞ ) , with additional regularity of the initial density on the basis of maximal regularity for the linearized system.

Keywords: compressible fluid; viscous fluid; capillarity; Korteweg type; local solvability; general domain; maximal regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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