Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Well-posedness and Regularity of Weak Solutions to the Prandtl's
  System   We continue our study on the global solution to the two-dimensional Prandtl's
system for unsteady boundary layers in the class considered by Oleinik provided
that the pressure is favorable. First, by using a different method from [13],
we gave a direct proof of existence of a global weak solution by a direct BV
estimate. Then we prove the uniqueness and continuous dependence on data of
such a weak solution to the initial-boundary value problem. Finally, we show
the smoothness of the weak solutions and then the global existence of smooth
solutions.

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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph