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Zbl 1141.76053
Kotschote, Matthias
Strong solutions for a compressible fluid model of Korteweg type. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 4, 679-696 (2008). ISSN 0294-1449

Summary: We prove existence and uniqueness of local strong solutions for an isothermal model of capillary compressible fluids derived by {\it J. E. Dunn} and {\it J. Serrin} [Arch. Ration. Mech. Anal. 88, No. 2, 95--133 (1985; Zbl 0582.73004)]. 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 $\cal H^\infty$-calculus. For these steps, it is decisive to find conditions on the inhomogeneities that are necessary and sufficient.

MSC 2000:: *76N10 Compressible fluids, general
35Q35 Other equations arising in fluid mechanics

Keywords: maximal regularity; $\cal H^\infty$-calculus; contraction mapping principle

Citations: Zbl 0582.73004

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