Abstract.
A global-in-time unique smooth solution is constructed for the Cauchy problem of the Navier—Stokes equations in the plane when initial velocity field is merely bounded not necessary square-integrable. The proof is based on a uniform bound for the vorticity which is only valid for planar flows. The uniform bound for the vorticity yields a coarse globally-in-time a priori estimate for the maximum norm of the velocity which is enough to extend a local solution. A global existence of solution for a q-th integrable initial velocity field is also established when \( q > 2 \).
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Accepted: November 26, 2000
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Giga, Y., Matsui, S. & Sawada, O. Global Existence of Two-Dimensional Navier—Stokes Flow with Nondecaying Initial Velocity. J. math. fluid mech. 3, 302–315 (2001). https://doi.org/10.1007/PL00000973
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DOI: https://doi.org/10.1007/PL00000973