TY - JOUR

T1 - Convergence of the vanishing viscosity approximation for superpositions of confined eddies

AU - Lopes Filho, M. C.

AU - Nussenzveig Lopes, H. J.

AU - Zheng, Yuxi

PY - 1999

Y1 - 1999

N2 - A confined eddy is a circularly symmetric flow with vorticity of compact support and zero net circulation. Confined eddies with disjoint supports can be super-imposed to generate stationary weak solutions of the two-dimensional incompressible inviscid Euler equations. In this work, we consider the unique weak solution of the two-dimensional incompressible Navier-Stokes equations having a disjoint superposition of very singular confined eddies as the initial datum. We prove the convergence of these weak solutions back to the initial configuration, as the Reynolds number goes to infinity. This implies that the stationary superposition of confined eddies with disjoint supports is the unique physically correct weak solution of the two-dimensional incompressible Euler equations.

AB - A confined eddy is a circularly symmetric flow with vorticity of compact support and zero net circulation. Confined eddies with disjoint supports can be super-imposed to generate stationary weak solutions of the two-dimensional incompressible inviscid Euler equations. In this work, we consider the unique weak solution of the two-dimensional incompressible Navier-Stokes equations having a disjoint superposition of very singular confined eddies as the initial datum. We prove the convergence of these weak solutions back to the initial configuration, as the Reynolds number goes to infinity. This implies that the stationary superposition of confined eddies with disjoint supports is the unique physically correct weak solution of the two-dimensional incompressible Euler equations.

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U2 - 10.1007/s002200050556

DO - 10.1007/s002200050556

M3 - Article

AN - SCOPUS:0033426837

SN - 0010-3616

VL - 201

SP - 291

EP - 304

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -