IUMJ

Title: Existence and time-asymptotics of global strong solutions to dynamic Korteweg models

Authors: Matthias Kotschote

Issue: Volume 63 (2014), Issue 1, 21-51

Abstract:

In this paper, we investigate isothermal and non-iso\-ther\-mal models of capillary compressible fluids as derived by J.\:E. Dunn and J. Serrin (1985). We establish global existence and uniqueness for initial data near equilibria, and show exponential stability of equilibrias in the phase space. The proof is based on maximal $L_p$-regularity results for the associated linear problem.