Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An energy method for rough partial differential equations   We present a well-posedness and stability result for a class of nondegenerate
linear parabolic equations driven by rough paths. More precisely, we introduce
a notion of weak solution that satisfies an intrinsic formulation of the
equation in a suitable Sobolev space of negative order. Weak solutions are then
shown to satisfy the corresponding energy estimates which are deduced directly
from the equation. Existence is obtained by showing compactness of a suitable
sequence of approximate solutions whereas uniqueness relies on a doubling of
variables argument and a careful analysis of the passage to the diagonal. Our
result is optimal in the sense that the assumptions on the deterministic part
of the equation as well as the initial condition are the same as in the
classical PDEs theory.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph