Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delayed Blow-Up for Chemotaxis Models with Local Sensing   The aim of this paper is to analyze a model for chemotaxis based on a local
sensing mechanism instead of the gradient sensing mechanism used in the
celebrated minimal Keller-Segel model. The model we study has the same entropy
as the minimal Keller-Segel model, but a different dynamics to minimize this
entropy. Consequently, the conditions on the mass for the existence of
stationary solutions or blow-up are the same, however we make the interesting
observation that with the local sensing mechanism the blow-up in the case of
supercritical mass is delayed to infinite time. Our observation is made
rigorous from a mathematical point via a proof of global existence of weak
solutions for arbitrary large masses and space dimension. The key difference of
our model to the minimal Keller-Segel model is that the structure of the
equation allows for a duality estimate that implies a bound on the
$(H^1)'$-norm of the solutions, which can only grow with a square-root law in
time. This additional $(H^1)'$-bound implies a lower bound on the entropy,
which contrasts markedly with the minimal Keller-Segel model for which it is
unbounded from below in the supercritical case. Besides, regularity and
uniqueness of solutions are also studied.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an