Global Navier–Stokes Flows for Non-decaying Initial Data with Slowly Decaying Oscillation

Consider the Cauchy problem of incompressible Navier–Stokes equations in 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...

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