Локальные Формулы Для Гидродинамического Давления И Их Приложения

Given any solution u of the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure p is twice as regular as u. This generalizes a recent result by Isett (2003 arXiv:1307.056517) (see also Colombo and De Rosa (2020 SIAM J. Math. Anal. 52 221-238)), which covers the case of Hölder spaces.

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Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations

Colombo¹,

Rosa²

2020

SIAM J. Math. Anal.

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In this work we investigate some regularization properties of the incompressible Euler equations and of the fractional Navier-Stokes equations where the dissipative term is given by (−∆) α , for a suitable power α ∈ (0, 1 2 ) (the only meaningful range for this result). Assuming that the solution u ∈ L ∞ t (C θ x ) for some θ ∈ (0, 1) we prove that u ∈ C θ t,x , the pressure p ∈ C 2θ− t,x and the kinetic energy e ∈ C 2θ 1−θ t . This result was obtained for the Euler equations in [Is13] with completely different arguments and we believe that our proof, based on a regularization and a commutator estimate, gives a simpler insight on the result.

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Локальные Формулы Для Гидродинамического Давления И Их Приложения

Cited by 3 publications

References 8 publications

Lipschitz Continuity of Solutions to Drift-Diffusion Equations in the Presence of Nonlocal Terms

Lipschitz Continuity of Solutions to Drift-Diffusion Equations in the Presence of Nonlocal Terms

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations

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