Strong solutions for a compressible fluid model of Korteweg type

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2008
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Zusammenfassung

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.

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510 Mathematik
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Korteweg model, Compressible fluids, Parabolic systems, Maximal regularity, H∞-calculus, Inhomogeneous boundary conditions
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ISO 690KOTSCHOTE, Matthias, 2008. Strong solutions for a compressible fluid model of Korteweg type. In: Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 2008, 25(4), pp. 679-696. ISSN 0294-1449. eISSN 1873-1430. Available under: doi: 10.1016/j.anihpc.2007.03.005
BibTex
@article{Kotschote2008Stron-25498,
  year={2008},
  doi={10.1016/j.anihpc.2007.03.005},
  title={Strong solutions for a compressible fluid model of Korteweg type},
  number={4},
  volume={25},
  issn={0294-1449},
  journal={Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
  pages={679--696},
  author={Kotschote, Matthias}
}
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