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arXiv · 2507.02923

Functional Reformulation of the Continuity Equation in Gases with Constant Density and its Application to the Existence Problem of Smooth Solutions to the Navier Stokes System

Ernesto D. Aguirre
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Abstract

We propose a rigorous reformulation of the incompressible Navier Stokes equations, starting from the energy equation and the ideal gas law. This reformulation allows the definition of a functional over the pressure field, which is used to bound the viscous dissipation term. It is shown that this norm can replace classical regularity criteria and serves as the foundation for a complete functional framework that includes local existence, singularity control, variational formulation, and uniqueness conditions.

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Ernesto D. Aguirre. 2025-06-25. Functional Reformulation of the Continuity Equation in Gases with Constant Density and its Application to the Existence Problem of Smooth Solutions to the Navier Stokes System. https://arxiv.org/abs/2507.02923

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