Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy
Acta Mathematica Sinica, English Series(2023)
摘要
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_xxxx + ∂ _xx|h_x|^α = f. It is shown that when 5/3 ≤α < 7/3 , the 3α - 5α - 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.
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关键词
Surface growth model,modified Navier–Stokes equations,partial regularity,Hausdorff dimension
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