Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the second iterate for active scalar equations   We consider an iterative resolution scheme for a broad class of active scalar
equations with a fractional power \gamma of the Laplacian and focus our
attention on the second iterate. The main objective of our work is to analyze
boundedness properties of the resulting bilinear operator, especially in the
super-critical regime. Our results are two-fold: we prove continuity of the
bilinear operator in BMO^{1-2\gamma} - a fractional analogue of the Koch-Tataru
space; for equations with an even symbol we show that the
B^{-\gamma}_{\infty,q} -regularity, where q > 2, is in a sense a minimal
necessary requirement on the solution.

32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg