L^∞-Estimates of the Solution of the Navier-Stokes Equations for a Nondecaying Initial Data

2019/07/06 by Santosh Pathak, Pathak, Santosh · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1907.03099

arxiv created 2019/07/06 · openalex publication_date 2019/07/06 · arxiv updated 2019/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we reprove the principal result of a paper by H-O Kreiss and Jens Lorenz from a different approach than the method proposed in their paper. More precisely, we consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝⁿ for n ≥ 3 with non-decaying initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is also an extension of their paper to higher dimension.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

Cited by

• A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations for the periodic initial data

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