Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Is the stochastic parabolicity condition dependent on $p$ and $q$?   In this paper we study well-posedness of a second order SPDE with
multiplicative noise on the torus $\T =[0,2\pi]$. The equation is considered in
$L^p(\O\times(0,T);L^q(\T))$ for $p,q\in (1, \infty)$. It is well-known that if
the noise is of gradient type, one needs a stochastic parabolicity condition on
the coefficients for well-posedness with $p=q=2$. In this paper we investigate
whether the well-posedness depends on $p$ and $q$. It turns out that this
condition does depend on $p$, but not on $q$. Moreover, we show that if $1<p<2$
the classical stochastic parabolicity condition can be weakened.

19
The categories of this paper are: eess
3
The categories of this paper are: physics
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th