Local well-posedness of unsteady potential flows near a space corner of right angle
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
Original language | English |
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Pages (from-to) | 104-169 |
Journal / Publication | Journal of Differential Equations |
Volume | 347 |
Online published | 30 Nov 2022 |
Publication status | Published - 25 Feb 2023 |
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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
Citation Format(s)
Local well-posedness of unsteady potential flows near a space corner of right angle. / Fang, Beixiang; Xiang, Wei; Xiao, Feng.
In: Journal of Differential Equations, Vol. 347, 25.02.2023, p. 104-169.
In: Journal of Differential Equations, Vol. 347, 25.02.2023, p. 104-169.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review