Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The initial value problem for the binormal flow with rough data   In this article we consider the initial value problem of the binormal flow
with initial data given by curves that are regular except at one point where
they have a corner. We prove that under suitable conditions on the initial data
a unique regular solution exists for strictly positive and strictly negative
times. Moreover, this solution satisfies a weak version of the equation for all
times and can be seen as a perturbation of a suitably chosen self-similar
solution. Conversely, we also prove that if at time t = 1 a small regular
perturbation of a self-similar solution is taken as initial condition then
there exists a unique solution that at time t = 0 is regular except at a point
where it has a corner with the same angle as the one of the self-similar
solution. This solution can be extended for negative times. The proof uses the
full strength of the previous papers [9], [2], [3] and [4] on the study of
small perturbations of self-similar solutions. A compactness argument is used
to avoid the weighted conditions we needed in [4], as well as a more refined
analysis of the asymptotic in time and in space of the tangent and normal
vectors.

4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol