A finite time result for vanishing viscosity in the plane with nondecaying vorticity
Abstract
Description
Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the Euler equations as viscosity approaches zero. We also establish a rate of convergence.
This version replaces a previous version (v1) which used an incorrect characterization of BMO. In this version we assume initial velocity has finite energy, and with this additional assumption we prove the same result as that in the previous version. The rate of convergence is now different, and the proof of the result has been modified considerably
This version replaces a previous version (v1) which used an incorrect characterization of BMO. In this version we assume initial velocity has finite energy, and with this additional assumption we prove the same result as that in the previous version. The rate of convergence is now different, and the proof of the result has been modified considerably