**SMS scnews item created by Daniel Daners at Mon 27 Feb 2012 2127**

Type: Seminar

Modified: Mon 27 Feb 2012 2132

Distribution: World

Expiry: 5 Mar 2012

**Calendar1: 5 Mar 2012 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@d220-237-40-101.mas801.nsw.optusnet.com.au (ddan2237) in SMS-WASM

### PDE Seminar

# Existence and uniqueness theorem of weak solutions to the parabolic-elliptic Keller-Segel system

### Kozono

Hideo Kozono

Tohoku University, Japan

5th March 2012, 2-3pm, Carslaw 829 (Access Grid Room)

## Abstract

In \(\mathbb R^n\) (\(n \geq 3\)), we first define a notion of weak
solutions to the Keller-Segel system of parabolic-elliptic type in the
scaling invariant class \(L^s((0,T); L^r(\mathbb R^n))\) for \(2/s + n/r =
2\) with \(n/2 < r < n\). Any condition on derivatives of solutions is
not required at all. The local existence theorem of weak solutions is
established for every initial data in \(L^{n/2}(\mathbb R^n)\). We
prove also their uniqueness. As for the marginal case when \(r = n/2\),
we show that if \(n \geq 4\), then the class \(C([0, T); L^{n/2}(\mathbb
R^n))\) enables us to obtain the only weak solution.

Check also the PDE
Seminar page. Enquiries to Florica
Cîrstea or Daniel Daners.