Munnier, Alexandre; Ramdani, Karim Asymptotic analysis of a Neumann problem in a domain with cusp. Application to the collision problem of rigid bodies in a perfect fluid. (English) Zbl 1333.35208 SIAM J. Math. Anal. 47, No. 6, 4360-4403 (2015). The authors consider a contact-collision problem between a solid immersed in a cavity filled with a perfect fluid and the bottom of the cavity. The problem reduces to a singular limit problem with a small parameter \(\varepsilon\) modelling the solid-cavity distance when \(\varepsilon\to 0\), for an elliptic problem posed in a domain \(\Omega_{\varepsilon}\) with mixed Dirichlet-Neumann boundary conditions. The domain converges to a singular domain with cusps and the problem is supposed to be axisymmetric. If \(\alpha>0\) denotes the tangency exponent (a parameter characterizing the contact point), the authors prove that for \(\alpha<2\) the limit solution has finite energy. Instead, for \(\alpha\geq 2\) the limit energy is unbounded and the type of blow-up is different if \(\alpha=2\) or if \(\alpha>2\). Reviewer: Bernard Ducomet (Bruyères le Châtel) Cited in 1 ReviewCited in 8 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 35J25 Boundary value problems for second-order elliptic equations 35J20 Variational methods for second-order elliptic equations 35C20 Asymptotic expansions of solutions to PDEs 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 35B44 Blow-up in context of PDEs Keywords:Dirichlet-Neumann; cusp; fluid-structure interaction; collision PDFBibTeX XMLCite \textit{A. Munnier} and \textit{K. Ramdani}, SIAM J. Math. Anal. 47, No. 6, 4360--4403 (2015; Zbl 1333.35208) Full Text: DOI arXiv References: [1] G. Acosta, M. G. Armentano, R. G. Durán, and A. L. 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