Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$

Ulisse Iotti

doi:10.5281/zenodo.14977034

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arXiv · 2503.03991

Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$

Ulisse Iotti

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Abstract

This paper investigates the extendability of local solutions for incompressible 3D Navier-Stokes and 3D Euler problems, with initial data $\mathbf{u}_0$ in the Sobolev space $H^s (\mathbb{R}^3)$, where $s$ ensures the existence and uniqueness of classical solutions. A geometric decomposition of the configuration space, identified by the orthogonality between the solution $\mathbf{u}$ and the pressure forces $\nabla p$, splits the problem into two simpler subproblems, which enable the uniform boundedness of the solution in each component of the partition, thereby ensuring the extendability of the solution.

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Ulisse Iotti. 2025-03-06. Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$. https://doi.org/10.5281/zenodo.14977034

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