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Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy.
- Source :
-
Acta Mathematica Sinica . Nov2023, Vol. 39 Issue 11, p2219-2246. 28p. - Publication Year :
- 2023
-
Abstract
- In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameter α in the nonlinear term in the following parabolic equation h t + h x x x x + ∂ x x | h x | α = f. It is shown that when 5 / 3 ≤ α < 7 / 3 , the 3 α − 5 α − 1 dimensional parabolic Hausdorff measure of S is zero, which generalizes the recent corresponding work of Ozánski and Robinson in [SIAM J. Math. Anal., 51, 228–255 (2019)] for α = 2 and f = 0. The same result is valid for a 3D modified Navier–Stokes system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 39
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 173557161
- Full Text :
- https://doi.org/10.1007/s10114-023-2458-2