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# 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} }