Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial regularity of suitable weak solutions of the model arising in
  amorphous molecular beam epitaxy   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 $\alpha$ in the nonlinear term in the
following parabolic equation $$h_t+h_{xxxx}+\partial_{xx}|h_x|^\alpha=f.$$ It
is shown that when $5/3\leq\alpha<7/3$, the
$\frac{3\alpha-5}{\alpha-1}$-dimensional parabolic Hausdorff measure of
$\mathcal{S}$ is zero, which generalizes the recent corresponding work of
Oz\'anski and Robinson in [31,SIAM J. Math. Anal. 51: 228--255, 2019] for
$\alpha=2$ and $f=0$. The same result is valid for a 3D modified Navier-Stokes
system.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg