Schwartz Function Valued Solutions of the Euler and the Navier-Stokes Equations

Philipp J. di Dio

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arXiv · 1912.11705

Schwartz Function Valued Solutions of the Euler and the Navier-Stokes Equations

Philipp J. di Dio

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Abstract

We prove the existence of a solution for the second order system of partial differential equations $\partial_t f = \nu\cdot\Delta f + g\cdot\nabla f + h\cdot f + k$ by a Montel space version of Arzel\`a--Ascoli and bound all Schwartz semi-norms. We find that for the Euler and the Navier--Stokes equations the vorticity remains a Schwartz function as long as the classical solution exists. Our approach is not affected by viscosity. It treats the hyperbolic Euler and the parabolic Navier--Stokes equation simultaneously.

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Philipp J. di Dio. 2019-12-25. Schwartz Function Valued Solutions of the Euler and the Navier-Stokes Equations. https://arxiv.org/abs/1912.11705

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