Existence, uniqueness and smoothness of a solution for 3D Navier-Stokes equations with any smooth initial velocity. A priori estimate of this solution

2014/03/14 by A. Tsionskiy, Tsionskiy, A., M. Tsionskiy +1
Mathematics · #35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q30 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1403.3475

29 pages. arXiv admin note: substantial text overlap with arXiv:1201.1609, arXiv:1101.0801

arxiv created 2022/08/18 · arxiv updated 2022/08/22

Abstract

Solutions of the Navier-Stokes and Euler equations with initial conditions for 2D and 3D cases were obtained in the form of converging series, by an analytical iterative method using Fourier and Laplace transforms \citeTT10,TT11. There the solutions are infinitely differentiable functions, and for several combinations of parameters numerical results are presented. This article provides a detailed proof of the existence, uniqueness and smoothness of the solution of the Cauchy problem for the 3D Navier-Stokes equations with any smooth initial velocity. When the viscosity tends to zero, this proof applies also to the Euler equations. A priori estimate of this solution is presented.

Citations

• Existence, uniqueness and smoothness of solution for 3D Navier-Stokes equations with any smooth initial velocity
• The Cauchy problem for the 3D Navier - Stokes equations. New approach to the solution and its justification

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