Global Navier-Stokes Flows for Non-decaying Initial Data with Slowly Decaying Oscillation
Abstract
Consider the Cauchy problem of incompressible Navier-Stokes equations in R3 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 Lp with finite p. In this paper, we construct global weak solutions for non-decaying initial data whose local oscillations decay, no matter how slowly.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- February 2020
- DOI:
- 10.1007/s00220-020-03695-3
- Bibcode:
- 2020CMaPh.375.1665K