Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential self-similar mixing and loss of regularity for continuity
  equations   We consider the mixing behaviour of the solutions of the continuity equation
associated with a divergence-free velocity field. In this announcement we
sketch two explicit examples of exponential decay of the mixing scale of the
solution, in case of Sobolev velocity fields, thus showing the optimality of
known lower bounds. We also describe how to use such examples to construct
solutions to the continuity equation with Sobolev but non-Lipschitz velocity
field exhibiting instantaneous loss of any fractional Sobolev regularity.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph