Stability of a class of exact solutions of the incompressible Euler equation in a disk

Guodong Wang

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arXiv · 2408.15598

Stability of a class of exact solutions of the incompressible Euler equation in a disk

Guodong Wang

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Abstract

We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument.

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Guodong Wang. 2024-08-28. Stability of a class of exact solutions of the incompressible Euler equation in a disk. https://arxiv.org/abs/2408.15598

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