Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-uniqueness in law of three-dimensional Navier-Stokes equations
  diffused via a fractional Laplacian with power less than one half   Non-uniqueness of three-dimensional Euler equations and Navier-Stokes
equations forced by random noise, path-wise and more recently even in law, have
been proven by various authors. We prove non-uniqueness in law of the
three-dimensional Navier-Stokes equations forced by random noise and diffused
via a fractional Laplacian that has power between zero and one half. The
solution we construct has H$\ddot{\mathrm{o}}$lder regularity with a small
exponent rather than Sobolev regularity with a small exponent. For the power
sufficiently small, the non-uniqueness in law holds at the level of Leray-Hopf
regularity. In particular, in order to handle transport error, we consider
phase functions convected by not only a mollified velocity field but a sum of
that with a mollified Ornstein-Uhlenbeck process if noise is additive and a
product of that with a mollified exponential Brownian motion if noise is
multiplicative.

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The categories of this paper are: chem-ph
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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: cmp-lg
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The categories of this paper are: q-fin
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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: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int