Article Contents
Article Contents

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

• * Corresponding author: Keyan Wang

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

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

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

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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