Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical local well-posedness for the fully nonlinear Peskin problem   We study the problem where a one-dimensional elastic string is immersed in a
two-dimensional steady Stokes fluid. This is known as the Stokes immersed
boundary problem and also as the Peskin problem. We consider the case with
equal viscosities and with a fully non-linear tension law; this model has been
called the fully nonlinear Peskin problem. In this case we prove local in time
well-posedness for arbitrary initial data in the scaling critical Besov space
$\dot{B}^{3/2}_{2,1}(\mathbb{T} ; \mathbb{R}^2)$. We additionally prove the
optimal higher order smoothing effects for the solution. To prove this result
we derive a new formulation of the boundary integral equation that describes
the parametrization of the string, and we crucially utilize a new cancellation
structure.

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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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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: acc-phys
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The categories of this paper are: nucl-th
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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: funct-an