The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity

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dc.creatorKelliher, James P.
dc.date2004-09-03
dc.date.accessioned2026-07-07T06:28:48Z
dc.date.available2026-07-07T06:28:48Z
dc.descriptionChemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler equations, convergence being uniform over any finite time interval. Yudovich, assuming an initial vorticity lying in L^p for all p >= q for some q, established the uniqueness of solutions to the Euler equations for an incompressible fluid in a bounded domain of n-space assuming a particular bound on the growth of the L^p-norm of the initial vorticity as p grows large. We combine these two approaches to establish, in the plane, the uniqueness of solutions to the Euler equations and the same zero-viscosity convergence as Chemin, but under Yudovich's assumptions on the vorticity with q = 2. The resulting bounded rate of convergence can be arbitrarily slow as a function of the viscosity.
dc.descriptionWill appear in Mathematical Research Letters volume 11 number 4
dc.identifierhttps://arxiv.org/abs/math-ph/0409011
dc.identifierhttp://arxiv.org/abs/math-ph/0409011
dc.identifierMathematical Research Letters, Vol 11(4) 2004 519-528
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97824
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject76D09
dc.titleThe inviscid limit for two-dimensional incompressible fluids with unbounded vorticity
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