Existence and smoothness of the Navier-Stokes equations and semigroups of linear operators

2022/09/14 by Yu. N. Kosovtsov, Kosovtsov, Yu. N. · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.06587

openalex publication_date 2022/09/14 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28

Abstract

Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the Navier-Stokes equations is given. It is shown that the introduced linear operator for Leray's equations is the generator of one-parameter contraction semigroup. This semigroup yields the existence of a unique and smooth classical solution of the associated Cauchy problem of Navier-Stokes equations in space ℝ³ under smooth initial conditions.

Cited by

• On Geometric Evolution and Microlocal Regularity of the Navier-Stokes Equations

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