论文标题
在无定形分子束外延中产生的模型合适弱解的部分规律性
Partial regularity of suitable weak solutions of the model arising in amorphous molecular beam epitaxy
论文作者
论文摘要
In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set $\mathcal{S}$ of suitable weak solutions and the parameter $α$ in the nonlinear term in the following parabolic equation $$h_t+h_{xxxx}+\partial_{xx}|h_x|^α=f.$$ It is shown that when $ 5/3 \leqα<7/3 $，$ \ frac {3α-5} {α-1} $ - $ \ Mathcal {s} $的尺寸抛物线抛物线率为Hausdorff度量为零，它概括了Ozánski和Robinson在[31，Siam siam siam siam siam J. Maths inozánskiand Robinson in the Maths ofozánski和Robinson的最新相应工作。肛门。 51：228--255，2019]，$α= 2 $和$ f = 0 $。相同的结果对于3D修改的Navier-Stokes系统有效。
In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set $\mathcal{S}$ of suitable weak solutions and the parameter $α$ in the nonlinear term in the following parabolic equation $$h_t+h_{xxxx}+\partial_{xx}|h_x|^α=f.$$ It is shown that when $5/3\leqα<7/3$, the $\frac{3α-5}{α-1}$-dimensional parabolic Hausdorff measure of $\mathcal{S}$ is zero, which generalizes the recent corresponding work of Ozánski and Robinson in [31,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.
