Local well-posedness of unsteady potential flows near a space corner of right angle

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Original languageEnglish
Pages (from-to)104-169
Journal / PublicationJournal of Differential Equations
Volume347
Online published30 Nov 2022
Publication statusPublished - 25 Feb 2023

Abstract

In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a cornered-space domain. The corner singularity is the key difficulty in establishing the local well-posedness of the problem. Moreover, the boundary conditions on both edges of the corner angle are of Neumann-type and fail to satisfy the linear stability condition, which makes it more difficult to establish a priori estimates on the boundary terms in the analysis. In this paper, extension methods will be updated to deal with the corner singularity, and, based on a key observation that the boundary operators are co-normal, new techniques will be developed to control the boundary terms.

Research Area(s)

  • Co-normal boundary condition, Corner singularity, Local well-posedness, Potential flow equations, Quasi-linear hyperbolic equation

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