Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity

Hirokazu Saito
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Hirokazu Saito: Graduate School of Informatics and Engineering, The University of Electro-Communications, 5-1 Chofugaoka 1-Chome, Chofu, Tokyo 182-8585, Japan

Mathematics, 2021, vol. 9, issue 7, 1-43

Abstract: The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible viscous flow with a sharp interface that is close to the hyperplane x N = 0 in the N -dimensional Euclidean space, N ? 2 . It is well-known that the Rayleigh–Taylor instability occurs when the upper fluid is heavier than the lower one, while this paper assumes that the lower fluid is heavier than the upper one and proves time-decay estimates of L p - L q type for the linearized equations. Our approach is based on solution formulas for a resolvent problem associated with the linearized equations.

Keywords: two-phase flow; semigroup; L p -L q decay estimate; surface tension; gravity; resolvent problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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