Non-Smooth Solutions of the Navier-Stokes Equation
J. Glimm, J. Petrillo
TL;DR
This paper constructs non-smooth Leray-Hopf solutions to the Navier-Stokes equation in a finite periodic domain, demonstrating finite-time blowup using analyticity and turbulent initial data characterized by spherical harmonics.
Contribution
It introduces a method to construct non-smooth solutions with finite-time blowup for the Navier-Stokes equation in a periodic setting, focusing on entropy-maximizing turbulent initial data.
Findings
Existence of non-smooth Leray-Hopf solutions in T3
Finite time blowup demonstrated using analyticity properties
Turbulent initial data characterized via spherical harmonics
Abstract
Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The construction occurs in a finite periodic cube T3. Entropy production maximizing solutions with turbulent initial data are selected. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation
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