Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Solvability in Functional Spaces for Smooth Nonsingular Vector
  Fields in the Plane   We address some global solvability issues for classes of smooth nonsingular
vector fields $L$ in the plane related to cohomological equations $Lu=f$ in
geometry and dynamical systems. The first main result is that $L$ is not
surjective in $C^\infty(\R^2)$ iff the geometrical condition -- the existence
of separatrix strips -- holds. Next, for nonsurjective vector fields, we
demonstrate that if the RHS $f$ has at most infra-exponential growth in the
separatrix strips we can find a global weak solution $L^1_{loc}$ near the
boundaries of the separatrix strips. Finally we investigate the global
solvability for perturbations with zero order p.d.o. We provide examples
showing that our estimates are sharp.

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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph