Rigorous Numerical Verification of Uniqueness and Smoothness in a\n Surface Growth Model

2013/11/09 by Dirk Blömker, Blömker, Dirk, Christian Nolde +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1311.2205

openalex publication_date 2013/11/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Based on numerical data and a-posteriori analysis we verify rigorously the\nuniqueness and smoothness of global solutions to a scalar surface growth model\nwith striking similarities to the 3D Navier--Stokes equations, for certain\ninitial data for which analytical approaches fail. The key point is the\nderivation of a scalar ODE controlling the norm of the solution, whose\ncoefficients depend on the numerical data. Instead of solving this ODE\nexplicitly, we explore three different numerical methods that provide rigorous\nupper bounds for its solution\n

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