On Double Hölder regularity of the hydrodynamic pressure in bounded domains
نویسندگان
چکیده
Abstract We prove that the hydrodynamic pressure p associated to velocity $$u\in C^\theta (\Omega )$$ u ∈ C θ ( Ω ) , $$\theta \in (0,1)$$ 0 , 1 of an inviscid incompressible fluid in a bounded and simply connected domain $$\Omega \subset {\mathbb {R}}^d$$ ⊂ R d with $$C^{2+}$$ 2 + boundary satisfies $$p\in C^{\theta }(\Omega p for \le \frac{1}{2}$$ ≤ C^{1,2\theta -1}(\Omega - >\frac{1}{2}$$ > . Moreover, when $$\partial \Omega C^{3+}$$ ∂ 3 we almost double Hölder regularity C^{2\theta -}(\Omega holds even <\frac{1}{2}$$ < This extends improves recent result Bardos Titi (Philos Trans R Soc A, 2022) obtained planar case every dimension $$d\ge 2$$ ≥ it also doubles regularity. Differently from (2022), do not introduce new condition pressure, but instead work natural one. In boundary-free d -dimensional torus, show can be actually achieved under weaker assumption divergence is sufficiently regular, thus necessarily zero.
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2023
ISSN: ['0944-2669', '1432-0835']
DOI: https://doi.org/10.1007/s00526-023-02432-7