Compressible fluid model of Korteweg type with free boundary condition: model problem. (English) Zbl 1441.35199
Summary: The aim of this paper is to prove the existence of \(\mathcal{R}\)-bounded solution operator families for a resolvent problem on the upper half-space arising from a compressible fluid model of Korteweg type with free boundary condition. Such a compressible fluid model was derived by J. E. Dunn and J. Serrin [Arch. Ration. Mech. Anal. 88, 95–133 (1985; Zbl 0582.73004)] and studied by M. Kotschote [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 4, 679–696 (2008; Zbl 1141.76053)] as a boundary value problem with non-slip boundary condition.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35R35 | Free boundary problems for PDEs |
Keywords:
Korteweg model; compressible fluids; free boundary condition; half-space model problem; resolvent problem; \(\mathcal{R}\)-bounded solution operator familiesReferences:
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