Conca, Carlos; San Martín H., Jorge; Tucsnak, Marius Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. (English) Zbl 0954.35135 Commun. Partial Differ. Equations 25, No. 5-6, 1019-1042 (2000). The motion of a rigid body inside a fluid flow (given by Navier-Stokes equations) is considered. The form of the fluid domain depends on the solutions, then a free boundary problem is considered, in a non-cylindrical domain of \(\mathbb{R}^3\). The existence of local weak solutions of the penalized problem is proved. By passing to the limit in this last problem, the existence of at least one weak solution for the initial problem is shown. In a special case, the result is global in time. Some very interesting a priori estimates are given and the Faedo-Galerkin method is used. Reviewer: Gelu Paşa (Bucureşti) Cited in 87 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35D05 Existence of generalized solutions of PDE (MSC2000) 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids Keywords:Galerkin method; rigid body motion; Navier-Stokes equations; a priori estimates PDFBibTeX XMLCite \textit{C. Conca} et al., Commun. Partial Differ. Equations 25, No. 5--6, 1019--1042 (2000; Zbl 0954.35135) Full Text: DOI References: [1] Conca C, J.Math 20 pp 279– (1994) [2] Conca C, C. R. Acad. Sci Paris Sér.I Math., 328 pp 473– (2000) · Zbl 0937.76012 [3] Grandmont C, C. R. Acad. Sci Paris Sé I Math 326 pp 525– (1998) · Zbl 0924.76022 [4] Hopf E, Math. Nachr 4 pp 213– (1951) · Zbl 0042.10604 [5] Kolmogorov A N, PrenticeHall, 4 (1970) [6] Ladyzhenskaya O A, flows, Gordon and Breach 4 (1969) [7] Leray J, J.Math.Pures et Appl 13 pp 1– (1933) [8] DOI: 10.1007/BF03167757 · Zbl 0655.76022 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.