Existence and time-asymptotics of global strong solutions to dynamic Korteweg models Matthias Kotschote 76N1035K5235K5535L6535M10Korteweg modelcompressible viscous fluidsglobal solutionsstability 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. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5187 10.1512/iumj.2014.63.5187 en Indiana Univ. Math. J. 63 (2014) 21 - 51 state-of-the-art mathematics http://iumj.org/access/