Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Cauchy problem for the Muskat equation. II: Critical initial data   We prove that the Cauchy problem for the Muskat equation is well-posed
locally in time for any initial data in the critical space of Lipschitz
functions with three-half derivative in $L^2$. Moreover, we prove that the
solution exists globally in time under a smallness assumption.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
16
The categories of this paper are: stat