Long time existence for a slightly perturbed vortex sheet

DOI10.1002/cpa.3160390605zbMath0603.76039OpenAlexW2141754739MaRDI QIDQ3740422

Oscar Orellana, Russel E. Caflisch

Publication date: 1986

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160390605

zbMATH Keywords

existencesmooth solutionsinitial perturbationapproximate differential equationsingularity developmentBirkhoff's equationanalytical disturbanceflat two-dimensional vortex sheetformal perturbation analysis

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Vortex flows for incompressible inviscid fluids (76B47) Partial differential equations of mathematical physics and other areas of application (35Q99) Parallel shear flows in hydrodynamic stability (76E05)

Related Items

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering ⋮ A criterion for the equivalence of the Birkhoff-Rott and Euler descriptions of vortex sheet evolution ⋮ Unnamed Item ⋮ A Nearly Optimal Existence Result for Slightly Perturbed 3-D Vortex Sheets ⋮ On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: Illposedness near degenerate stationary solutions ⋮ Regularized Euler-\(\alpha \) motion of an infinite array of vortex sheets ⋮ Well-posedness of the free boundary problem in incompressible MHD with surface tension ⋮ A note on the abstract Cauchy-Kowalewski theorem ⋮ Vortex blob methods applied to interfacial motion ⋮ Viscous profiles of vortex patches ⋮ A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities ⋮ On vortex-sheet evolution beyond singularity formation ⋮ The influence of electric fields and surface tension on Kelvin-Helmholtz instability in two-dimensional jets ⋮ Singularity formation in three-dimensional vortex sheets ⋮ On Compressible and Incompressible Vortex Sheets ⋮ Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity ⋮ Local well-posedness for fluid interface problems ⋮ A nonlinear approximation for vortex sheet evolution and singularity formation ⋮ Remarks on stationary and uniformly-rotating vortex sheets: rigidity results ⋮ Numerical evidence of nonuniqueness in the evolution of vortex sheets ⋮ Singularity formation for complex solutions of the 3D incompressible Euler equations

Cites Work

• Unnamed Item