Strong solutions for a compressible fluid model of Korteweg type

Type of Publication: Journal article
Author: Kotschote, Matthias
Year of publication: 2008
Published in: Annales de l'Institut Henri Poincare (C) Non Linear Analysis ; 25 (2008), 4. - pp. 679-696. - ISSN 0294-1449. - eISSN 1873-1430
DOI (citable link): https://dx.doi.org/10.1016/j.anihpc.2007.03.005
Summary:
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.
MSC Classification: 76N10; 35K50; 35K55; 35L65; 35M10
Subject (DDC): 510 Mathematics
Keywords: Korteweg model, Compressible fluids, Parabolic systems, Maximal regularity, H∞-calculus, Inhomogeneous boundary conditions

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KOTSCHOTE, Matthias, 2008. Strong solutions for a compressible fluid model of Korteweg type. In: Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 25(4), pp. 679-696. ISSN 0294-1449. eISSN 1873-1430. Available under: doi: 10.1016/j.anihpc.2007.03.005

@article{Kotschote2008Stron-25498, title={Strong solutions for a compressible fluid model of Korteweg type}, year={2008}, doi={10.1016/j.anihpc.2007.03.005}, number={4}, volume={25}, issn={0294-1449}, journal={Annales de l'Institut Henri Poincare (C) Non Linear Analysis}, pages={679--696}, author={Kotschote, Matthias} }

2013-12-18T08:19:48Z Annales de l'Institut Henri Poincaré (C): Non Linear Analysis ; 25 (2008), 4. - S. - 679-696 terms-of-use Kotschote, Matthias eng Kotschote, Matthias 2013-12-18T08:19:48Z 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<sup>∞</sup>-calculus. For these steps, it is decisive to find conditions on the inhomogeneities that are necessary and sufficient. Strong solutions for a compressible fluid model of Korteweg type 2008

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