Desjardins, B.; Esteban, M. J. On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models. (English) Zbl 0953.35118 Commun. Partial Differ. Equations 25, No. 7-8, 1399-1413 (2000). Summary: The purpose of this note is to derive compactness properties for both incompressible and compressible viscous flows in a bounded domain interacting with a finite number of rigid bodies. We prove the global existence of weak solutions away from collisions. Cited in 1 ReviewCited in 86 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:fluid structure interaction; Navier-Stokes equations; global existence of weak solutions PDF BibTeX XML Cite \textit{B. Desjardins} and \textit{M. J. Esteban}, Commun. Partial Differ. Equations 25, No. 7--8, 1399--1413 (2000; Zbl 0953.35118) Full Text: DOI References: [1] DOI: 10.1007/BF01393835 · Zbl 0696.34049 [2] Errate D, C.R. Acad. Sci. Paris Ser. 1 Math 318 (3) pp 275– (1994) [3] DOI: 10.1007/s002050050043 · Zbl 0898.35071 [4] Grandmont C, Sci. Paris Ser. 1 Math 326 (4) pp 525– (1998) [5] Hoffmann K.H, J. Math. Pures Appl 13 (4) pp 331– (1934) [6] Lions P.L, Compressible Models [7] Reed , M and Simon , B . ”Analysis of operators”. · Zbl 0401.47001 [8] Serre D, Japan J. Math 4 (1) pp 33– (1987) [9] DOI: 10.1007/BF01094193 · Zbl 0639.76035 [10] Tartar L, Sci. Inst. Ser. C:Math. Phys. Sci 40 (1) pp 263– (1983) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.