On the periodic Navier--Stokes equation: An elementary approach to existence and smoothness for all dimensions $n\geq 2$
Philipp J. di Dio
Abstract:In this paper we study the periodic Navier-Stokes equation. From the periodic Navier-Stokes equation and the linear equation ∂tu = ν∆u + P[v∇u] we derive the corresponding equations for the time dependent Fourier coefficients a k (t). We prove the existence of a smooth solution u of the linear equation by a Montel space version of Arzelà-Ascoli. We gain bounds on the a k 's of u depending on v. These bounds provide the small time existence of a unique smooth solution of the Navier-Stokes equation. They prove t… Show more
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