Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions
arxiv(2024)
Abstract
We study the existence of strong solutions to the initial value problem for
the incompressible Navier-Stokes equations in ℝ^N, N≥ 3. Our
investigation shows that local in-time classical solutions do not develop
singularity as long as the initial velocity lies in (L^2(ℝ^N))^N∩
(L^∞(ℝ^N))^N.
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