Global well-posedness and long time behaviors of chemotaxis-fluid system modeling coral fertilization

Myeongju Chae; Kyungkeun Kang; Jihoon Lee

doi:10.3934/dcds.2020109

Article Contents

2020, Volume 40, Issue 4: 2135-2163. Doi: 10.3934/dcds.2020109

This issue Previous Article Global well-posedness, pattern formation and spiky stationary solutions in a Beddington–DeAngelis competition system Next Article Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions

Global well-posedness and long time behaviors of chemotaxis-fluid system modeling coral fertilization

1.
Department of Applied Mathematics and Institute for integrated Mathematical Sciences, Hankyong National University, Ansung, Korea
2.
Department of Mathematics, Yonsei University, Seoul, Korea
3.
Department of Mathematics, Chung-Ang University, Seoul, Korea

^* Corresponding author: Jihoon Lee
^* Corresponding author: Jihoon Lee

Received: April 2019

Revised: October 2019

Published: December 2019

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Abstract

We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the models as well as their temporal decays in two and three dimensions. We also show that the total masses of egg and sperm density have positive lower bounds as time tends to infinity in three dimensions.

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Mathematics Subject Classification: Primary: 35Q30, 35K57; Secondary: 76Dxx, 76Bxx.

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