## arXiv Analytics

### arXiv:0901.4359 [math.AP]AbstractReferencesReviewsResources

#### Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension

Published 2009-01-28Version 1

This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension $N$. The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It allows us to use of De Giorgi type methods introduced for elliptic regularity with rough coefficients. In spite these systems are entropy supercritical, it is possible to control the hypothetical blow-ups, in the critical scaling, via a very weak norm. Analogies with the Navier-Stokes equation are briefly discussed in the introduction.

Categories: math.AP, math-ph, math.MP
Related articles: Most relevant | Search more
arXiv:1609.03231 [math.AP] (Published 2016-09-11)
On the $L^p$ regularity of solutions to the generalized Hunter-Saxton system
arXiv:1712.02649 [math.AP] (Published 2017-12-06)
Global regularity for systems with $p$-structure depending on the symmetric gradient
arXiv:1602.04549 [math.AP] (Published 2016-02-15)
Global Regularity of 2D almost resistive MHD Equations