A Keller–Segel type system in higher dimensions
Suleyman Ulusoy
Department of Mathematics and Natural Sciences, American University of Ras Al Khaimah, Ras Al Khaimah, UAE
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Abstract
We analyze an equation that is gradient flow of a functional related to Hardy–Littlewood–Sobolev inequality in whole Euclidean space , . Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of “free-energy solutions”, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a critical value. Actually, there is a critical value of a parameter in the equation below which there is a global-in-time energy solution and above which there exist blowing-up energy solutions.
Cite this article
Suleyman Ulusoy, A Keller–Segel type system in higher dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 4, pp. 961–971
DOI 10.1016/J.ANIHPC.2016.08.002