Abstract
Consider the Cauchy problem of incompressible Navier–Stokes equations in \(\mathbb {R}^3\) with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a time-global weak solution has been known. However, such data do not include constants, and the only known global solutions for non-decaying data are either for perturbations of constants, or when the velocity gradients are in \(L^p\) with finite p. In this paper, we construct global weak solutions for non-decaying initial data whose local oscillations decay, no matter how slowly.
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The research of both Kwon and Tsai was partially supported by NSERC Grant 261356-13.
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Communicated by H. T. Yau
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Kwon, H., Tsai, TP. Global Navier–Stokes Flows for Non-decaying Initial Data with Slowly Decaying Oscillation. Commun. Math. Phys. 375, 1665–1715 (2020). https://doi.org/10.1007/s00220-020-03695-3
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DOI: https://doi.org/10.1007/s00220-020-03695-3