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Local well-posedness for Navier-Stokes equations with a class of ill-prepared initial data

  • * Corresponding author: Keyan Wang

    * Corresponding author: Keyan Wang 

The first author is supported by NSFC grant No. 11971290.

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  • In this paper, we prove that for the ill-prepared initial data of the form

    $ \begin{equation} \nonumber u_0^\epsilon(x) = (v_0^h(x_\epsilon), \epsilon^{-1}v_0^3(x_\epsilon))^T,\quad x_\epsilon = (x_h, \epsilon x_3)^T, \end{equation} $

    the Cauchy problem of the incompressible Navier-Stokes equations on $ \mathbb{R}^3 $ is locally well-posed for all $ \epsilon > 0 $, provided that the initial velocity profile $ v_0 $ is analytic in $ x_3 $ but independent of $ \epsilon $.

    Mathematics Subject Classification: Primary: 76D03, 76D05; Secondary: 35Q30.

    Citation:

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