Journal article
Interior second order Hölder regularity for Stokes systems
Journal of Differential Equations, Vol.438, 113407
09/2025
DOI: 10.1016/j.jde.2025.113407
Abstract
Global second order Hölder regularity for Stokes systems can be obtained by global Schauder estimates, which are actually a priori estimates and were established by Solonnikov [20] and [23] with appropriate compatible conditions. This paper will investigate the corresponding interior regularity which unfortunately may fail in general from Serrin's counterexample (cf. [19]). However, we discover interior C2,α regularity for velocity and interior C1,α regularity for pressure in spatial variables, and furthermore, for curl of velocity, we find its gradient belongs to Cα,α2, that is, possesses Hölder continuity in both space and time directions. The interesting phenomenon here is that no continuity in time variable is assumed for both the coefficients and the righthand side terms. The estimates for velocity and its curl are achieved pointwisely and the results are sharp indicated by a counterexample.
Details
- Title: Subtitle
- Interior second order Hölder regularity for Stokes systems
- Creators
- Rong Dong - Xi'an Jiaotong UniversityDongsheng Li - Xi'an Jiaotong UniversityLihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.438, 113407
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.jde.2025.113407
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Grant note
- xzy012022004 / Fundamental Research Funds for the Central Universities (https://doi.org/10.13039/501100012226) 12471202; 12001419 / National Natural Science Foundation of China (https://doi.org/10.13039/501100001809) 22JSZ003; 23JSQ026 / Shaanxi Fundamental Science Research Project for Mathematics and Physics
- Language
- English
- Date published
- 09/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984822960602771
Metrics
1 Record Views