Non-Smooth Solutions of the Navier-Stokes Equation and their Means

J. Glimm; J. Petrillo

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arXiv · 2410.09261

Non-Smooth Solutions of the Navier-Stokes Equation and their Means

J. Glimm·J. Petrillo

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Abstract

Non-smooth (finite time blowup) Leray-Hopf solutions of the incompressible Navier-Stokes equation are constructed. The initial data for blowup is characterized by nonzero energy related turbulent fluctuations. The construction occurs in a finite periodic cube T3. 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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J. Glimm, J. Petrillo. 2024-10-11. Non-Smooth Solutions of the Navier-Stokes Equation and their Means. https://arxiv.org/abs/2410.09261

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