The decay rates of solutions to a chemotaxis-shallow water system
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 17,p. 1-7
- https://doi.org/10.14232/ejqtde.2021.1.17
Abstract
In this paper, we consider the large time behavior of solution for the chemotaxis-shallow water system in R-2. The lower bound for time decay rates of the bacterial density and the chemoattractant concentration are proved by the method of energy estimates, which implies these two variables tend to zero at the L-2-rate (1 + t)(-1/2). Furthermore, by the Fourier splitting method, we also show the first order spatial derivatives of the bacterial density tends to zero at the L-2-rate (1 + t)(-1).Keywords
This publication has 24 references indexed in Scilit:
- An optimal result for global existence in a three-dimensional Keller–Segel–Navier–Stokes system involving tensor-valued sensitivity with saturationCalculus of Variations and Partial Differential Equations, 2019
- Global solvability and boundedness to a coupled chemotaxis-fluid model with arbitrary porous medium diffusionJournal of Differential Equations, 2018
- Global existence and large time behavior for a two-dimensional chemotaxis-Navier–Stokes systemJournal of Differential Equations, 2017
- On the existence of local strong solutions to chemotaxis–shallow water system with large data and vacuumJournal of Differential Equations, 2016
- Existence of smooth solutions to coupled chemotaxis-fluid equationsDiscrete & Continuous Dynamical Systems, 2013
- A Note on Global Existence for the Chemotaxis–Stokes Model with Nonlinear DiffusionInternational Mathematics Research Notices, 2012
- A coupled chemotaxis-fluid model: Global existenceAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2011
- Global Solutions to the Coupled Chemotaxis-Fluid EquationsCommunications in Partial Differential Equations, 2010
- COUPLED CHEMOTAXIS FLUID MODELMathematical Models and Methods in Applied Sciences, 2010
- L2 decay for weak solutions of the Navier-Stokes equationsArchive for Rational Mechanics and Analysis, 1985