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Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
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We rigorously construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewed as the vortex-patch counterpart of the well-known Lamb-Chaplygin dipole. Our construction is based on a novel fixed-point approach that determines the patch boundary as the fixed point of a certain nonlinear map. Smoothness and other properties of the patch boundary are also obtained.
Forward citations
Cited by 2 Pith papers
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Existence of analytic non-convex V-states
A rigorous computer-assisted proof establishes the existence of non-convex analytic uniformly rotating vortex patches with 6-fold symmetry for the 2D Euler equation.
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Stability for multiple Lamb dipoles
Finite sums of Lamb dipoles in the half-plane, with ordered speeds and well-separated initial positions, are Lyapunov stable under the 2D Euler equations.
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