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What is the regularity of solutions for the stationary incompressible Navier-Stokes equations \begin{align*} -\Delta u +u\cdot \nabla u + \nabla p &= 0\\ \nabla \cdot u &= 0 \end{align*} in $\mathbb R^2$? Where can I find a precise reference with an existence/uniqueness/regularity statement?

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    $\begingroup$ you asked the same question yesterday --- it was downvoted, you deleted it and now you ask again; if you wish to improve the question, please go ahead, but not by deletion. $\endgroup$ – Carlo Beenakker Jan 16 at 15:17
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The weak solution must be smooth. Galdi has a comprehensive book (more than 1000 pages) discussing stationary NS.

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