Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d


Journal Article

This paper establishes the hyper-contractivity in L∞(ℝd) (it's known as ultra-contractivity) for the multi-dimensional Keller-Segel systems with the diffusion exponent m > 1-2/d. The results show that for the super- critical and critical case 1-2/d < m ≤ 2-2/d, if ∥U0∥d(2-m)/2 < Cd, m where Cd, m is a universal constant, then for any t > 0 ∥u(.,t)∥L∞(ℝd) is bounded and decays as t goes to infinity. For the subcritical case m > 2-2/d, the solution u(.,t)∈ L∞(ℝd) with any initial data U0 ∈ L1+(ℝd) for any positive time.

Full Text

Duke Authors

Cited Authors

  • Bian, S; Liu, JG; Zou, C

Published Date

  • March 1, 2014

Published In

Volume / Issue

  • 7 / 1

Start / End Page

  • 9 - 28

Electronic International Standard Serial Number (EISSN)

  • 1937-5077

International Standard Serial Number (ISSN)

  • 1937-5093

Digital Object Identifier (DOI)

  • 10.3934/krm.2014.7.9

Citation Source

  • Scopus