Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularization by noise and flows of solutions for a stochastic heat
  equation   Motivated by the regularization by noise phenomenon for SDEs we prove
existence and uniqueness of the flow of solutions for the non-Lipschitz
stochastic heat equation $$\frac{\partial u}{\partial
t}=\frac12\frac{\partial^2 u}{\partial z^2} + b(u(t,z)) + \dot{W}(t,z), $$
where $\dot W$ is a space-time white noise on $\mathbb{R}_+\times\mathbb{R}$
and $b$ is a bounded measurable function on $\mathbb{R}$. As a byproduct of our
proof we also establish the so-called path--by--path uniqueness for any initial
condition in a certain class on the same set of probability one. This extends
recent results of Davie (2007) to the context of stochastic partial
differential equations.

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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: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: chem-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: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg