Kotschote, Matthias

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Strong solutions for a compressible fluid model of Korteweg type

2008, Kotschote, Matthias

We prove existence and uniqueness of local strong solutions for an isothermal model of capillary compressible fluids derived by J.E. Dunn and J. Serrin (1985). This nonlinear problem is approached by proving maximal regularity for a related linear problem in order to formulate a fixed point equation, which is solved by the contraction mapping principle. Localising the linear problem leads to model problems in full and half space, which are treated by Dore–Venni Theory, real interpolation and H-calculus. For these steps, it is decisive to find conditions on the inhomogeneities that are necessary and sufficient.