GLOBAL WEAK SOLUTIONS TO A CHEMOTAXIS-NAVIER-STOKES SYSTEM IN ℝ3

Kyungkeun Kang, Jihoon Lee, Michael Winkler

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The Cauchy problem in ℝ3for the chemotaxis-Navier 'Equation Presented' is considered. Under suitable conditions on the initial data (n0, c0, u0), with regard to the crucial first component requiring that n0∈ L1(ℝ3) be nonnegative and such that (n0+ 1) ln(n0+ 1) ∈ L1(ℝ3), a globally defined weak solution with (n. c, u)|t=0= (n0, c0, u0) is constructed. Apart from that, assuming that moreover ∫ℝ3n0(x) ln(1+|x|2)dx is finite, it is shown that a weak solution exists which enjoys further regularity features and preserves mass in an appropriate sense.

Original languageEnglish
Pages (from-to)5201-5222
Number of pages22
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume42
Issue number11
DOIs
Publication statusPublished - 2022 Nov

Bibliographical note

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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