Dept. Math, Hokkaido Univ. EPrints Server

On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data

Preprint Series # 860
Giga, Yoshikazu and Jo, Hideaki and Mahalov, Alex and Yoneda, Tsuyoshi On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data. (2007);

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Abstract

We consider the Navier-Stokes equations with the Coriolis force when intial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data is in $FM_0$, Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data is almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.

Item Type:Preprint
Uncontrolled Keywords:Navier-Stokes equations, analyticity, frequency set, Coriolis force
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1713