Abstract
The chemotaxis system
is considered in a bounded domain \(\Omega \subset \mathbb {R}^n\) with smooth boundary, where \(\chi >0\). An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter \(\chi \) with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that
for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that
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Lankeit, J., Winkler, M. A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data. Nonlinear Differ. Equ. Appl. 24, 49 (2017). https://doi.org/10.1007/s00030-017-0472-8
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DOI: https://doi.org/10.1007/s00030-017-0472-8