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arXiv · 2111.06550

Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6

Bian Wu
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Abstract

By using defect measures, we prove the existence of partially regular weak solutions to the stationary Navier-Stokes equations with external force $f \in L_{\text{loc}}^q \cap L^{3/2}, q>3$ in general open subdomains of $\mathbb{R}^6$. These weak solutions satisfy certain local energy estimates and we estimate the size of their singular sets in terms of Hausdorff measures. We also prove the defect measures vanish under a smallness condition, in contrast to the nonstationary Navier-Stokes equations in $\mathbb{R}^4 \times [0,\infty[$.

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Bian Wu. 2021-11-12. Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6. https://doi.org/10.1007/s00526-022-02273-w

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