Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky
  equations   We give a substantially simplified proof of near-optimal estimate on the
Kuramoto-Sivashinsky equation from [F. Otto, "Optimal bounds on the
Kuramoto-Sivashinsky equation", JFA 2009], at the same time slightly improving
the result. The result in the above cited paper relied on two ingredients: a
regularity estimate for capillary Burgers and an a novel priori estimate for
the inhomogeneous inviscid Burgers equation, which works out that in many ways
the conservative transport nonlinearity acts as a coercive term. It is the
proof of the second ingredient that we substantially simplify by proving a
modified K\'arm\'an-Howarth-Monin identity for solutions of the inhomogeneous
inviscid Burgers equation. This gives a new interpretation of the results
obtained in [F. Golse, B. Perthame "Optimal regularizing effect for scalar
conservation laws", Rev. Mat. Iber., 2013].

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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int