Interior Schauder estimates for Stokes systems in non-divergence form

Rong Dong; Dongsheng Li; Lihe Wang

doi:10.48550/arxiv.2401.09841

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Interior Schauder estimates for Stokes systems in non-divergence form

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Interior Schauder estimates for Stokes systems in non-divergence form

Rong Dong, Dongsheng Li and Lihe Wang

ArXiv.org

Cornell University

01/18/2024

DOI: 10.48550/arxiv.2401.09841

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

The global Schauder estimates for Stokes systems are established by Solonnikov [15] and [16] while the interior ones may fail generally from Serrin's counterexample (cf. [14]). Nevertheless, this paper obtains interior C2,α estimates for velocity and interior C1,α estimates for pressure in spatial direction. Furthermore, the Cα,α2 estimate is attained for derivatives of curl of velocity. The estimates for velocity can be achieved pointwisely. The results are sharp and surprising since no continuity in time variable is assumed for the coefficients and the righthand side terms.

Mathematics - Analysis of PDEs

Details

Title: Subtitle: Interior Schauder estimates for Stokes systems in non-divergence form
Creators: Rong Dong
Dongsheng Li
Lihe Wang
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2401.09841
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 01/18/2024
Academic Unit: Mathematics
Record Identifier: 9984548291302771

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