Strong solutions for a compressible fluid model of Korteweg type

Publikationstyp: Zeitschriftenartikel
Autor/innen: Kotschote, Matthias
Erscheinungsjahr: 2008
Erschienen in: Annales de l'Institut Henri Poincare (C) Non Linear Analysis ; 25 (2008), 4. - S. 679-696. - ISSN 0294-1449. - eISSN 1873-1430
DOI (zitierfähiger Link): https://dx.doi.org/10.1016/j.anihpc.2007.03.005
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.
MSC-Klassifikation: 76N10; 35K50; 35K55; 35L65; 35M10
Fachgebiet (DDC): 510 Mathematik
Schlagwörter: 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

@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 Kotschote, Matthias deposit-license eng Kotschote, Matthias 2013-12-18T08:19:48Z Strong solutions for a compressible fluid model of Korteweg type 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. 2008

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