Abstract
We consider weak solutions \((u,\pi ):{\Omega }\to \mathbb {R}^{n}\times \mathbb {R}\) to stationary ϕ-Navier-Stokes systems of the type \( \left \{ \begin {array}{ll} -\mathrm {div~} a(x,\mathcal {E} u)+\nabla \pi +[Du]u=f \\ \mathrm {div~} u=0 \end {array} \right . \) in \({\Omega }\subset \mathbb {R}^{n}\), and to the corresponding ϕ-Stokes systems, in which the convective term [Du]u does not appear. In the above system, the function a(x,ξ) depends Hölder continuously on x and satisfies growth conditions with respect to the second variable expressed through a Young function ϕ. The notation \(\mathcal {E} u\) is used for the symmetric part of the gradient Du. We prove results on the fractional higher differentiability of both the symmetric part of the gradient \(\mathcal {E} u\) and of the pressure π.
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Funding
Open Access funding enabled and organized by Projekt DEAL. The first and second authors are members of INdAM-GNAMPA and of UMI-TAA. The first and second authors were partially supported by FRA Project 2020 Regolarità per minimi di funzionali ampiamente degeneri (FRA-000022-ALTRI-CDA-7-5-2021-FRA-PASSARELLI) and by the INdAM–GNAMPA 2022 Project Enhancement e segmentazione immagini mediante operatori tipo campionamento e metodi variazionali, codice CUP_E55F22000270001.
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Giannetti, F., Passarelli di Napoli, A. & Scheven, C. Fractional Higher Differentiability for Solutions of Stationary Stokes and Navier-Stokes Systems with Orlicz Growth. Potential Anal 60, 647–672 (2024). https://doi.org/10.1007/s11118-023-10065-w
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DOI: https://doi.org/10.1007/s11118-023-10065-w