Dept. Math, Hokkaido Univ. EPrints Server

Large time behavior of derivatives of the vorticity for the two dimensional Navier-Stokes flow

Preprint Series # 716
maekawa, yasunori Large time behavior of derivatives of the vorticity for the two dimensional Navier-Stokes flow. (2005);

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Abstract

This paper studies the large time asymptotic behavior of derivatives of the vorticity solving the two-dimensional vorticity equations equivalent to the Navier-Stokes equations. It is well-known by now that the vorticity behaves asymptotically as the Oseen vortex provided that the initial vorticity is integrable. This paper shows that each derivative of the vorticity also behave asymptotically as that of the Oseen vortex. For the proof new spatial decay estimates for derivatives are established. These estimates control behavior at the space infinity. The convergence result follows from a rescaling and compactness argument.

Item Type:Preprint
Additional Information:40 copies recommender: Prof. Yoshikazu Giga
Uncontrolled Keywords:large time behavior, two-dimensional vorticity equations, Navier-Stokes equations
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:935