Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical exponent for evolution equation in Modulation space   In this paper, we propose a method to find the critical exponent for certain
evolution equations in modulation spaces. We define an index $\sigma (s,q)$,
and use it to determine the critical exponent of the fractional heat equation
as an example. We prove that when $\sigma (s,q)$ is greater than the critical
exponent, this equation is locally well posed in the space
$C(0,T;M_{p,q}^{s})$; and when $\sigma (s,q)$ is less than the critical
exponent, this equation is ill-posed in the space $C(0,T;M_{2,q}^{s})$. Our
method may further be applied to some other evolution equations.

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics