Large time behavior in a three-dimensional degenerate chemotaxis-Stokes system modeling coral fertilization

Liu, Ji

doi:10.1016/j.jde.2020.04.039

Cited by 7 publications

(1 citation statement)

References 48 publications

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“…For instance, in two‐dimensional bounded domain, Espejo and Winkler [11] firstly studied global existence and stabilization of solutions for () with

S(n)=n

in an incompressible Navier‐Stokes‐fluid effect. In the spatially three dimensional context, regardless for initial value problems or for initial‐boundary value problems associated with (), the global dynamical behaviors need to rely on appropriate smallness restrictions on initial data [12–15] or on some nonlinear mechanisms, such as saturation effects of gametes [14–17], signal‐dependent sensitivity [18, 19], porous medium diffusion [20], slow p ‐Laplacian diffusion [21, 22] or flux limitation [23].…”

Section: Introductionmentioning

confidence: 99%

On a three‐dimensional chemotaxis‐Stokes system with nonlinear sensitivity modeling coral fertilization

Zheng

2022

Z Angew Math Mech

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This paper is concerned with the effects of nonlinear sensitivity on boundedness of solutions for the following chemotaxis‐Stokes system trueleftntgoodbreak+boldu·∇ngoodbreak=∇·(∇n−Sfalse(nfalse)∇c)goodbreak−nm,rightfalse(x,tfalse)∈normalΩgoodbreak×false(0,∞false),leftctgoodbreak+boldu·∇cgoodbreak=normalΔcgoodbreak−cgoodbreak+m,rightfalse(x,tfalse)∈normalΩgoodbreak×false(0,∞false),leftmtgoodbreak+boldu·∇mgoodbreak=normalΔmgoodbreak−mn,rightfalse(x,tfalse)∈normalΩgoodbreak×false(0,∞false),leftutgoodbreak=normalΔboldugoodbreak+∇Pgoodbreak+(n+m)∇ϕ,rightfalse(x,tfalse)∈normalΩgoodbreak×false(0,∞false),left∇·boldugoodbreak=0,rightfalse(x,tfalse)∈normalΩgoodbreak×false(0,∞false),$$\begin{eqnarray*} \qquad\qquad\qquad\qquad\qquad{\left\lbrace \begin{aligned} &n_{t}+{\bf u}\cdot \nabla n=\nabla \cdot (\nabla n-S(n)\nabla c)-nm, &(x,t)\in \Omega \times (0,\infty ), \\ &c_{t}+{\bf u}\cdot \nabla c=\Delta c-c+m, &(x,t)\in \Omega \times (0,\infty ),\\ &m_{t}+{\bf u}\cdot \nabla m=\Delta m-mn, &(x,t)\in \Omega \times (0,\infty ), \\ &{\bf u}_{t}=\Delta {\bf u}+\nabla P+(n+m)\nabla \phi , &(x,t)\in \Omega \times (0,\infty ),\\ &\nabla \cdot {\bf u}=0, &(x,t)\in \Omega \times (0,\infty ), \end{aligned} \right.} \end{eqnarray*}$$in a smoothly bounded domain normalΩ⊂R3$\Omega \subset \mathbb {R}^{3}$ under no‐flux boundary conditions for n,c,m$n, c, m$ and no‐slip boundary conditions for u, where n and m denote the densities of unfertilized sperms and eggs, respectively, c stands for the concentration of the signal, u represents the velocity of fluid, P is the pressure within the fluid and ϕ is the gravitational potential. This system describes the process of coral fertilization occurring in ocean flow. Based on the novel conditional estimates for c and u, it is proved that for all appropriately regular nonnegative initial data, this system possesses a unique globally bounded solution provided that S∈C2(false[0,∞false))$S\in C^{2}([0,\infty ))$ satisfies S(n)≤χnfalse(n+1false)α−1$S(n)\le \chi n(n+1)^{\alpha -1}$ with χ>00.28emand0.28emα<1$\chi >0\;\text{and}\;\alpha <1$, which improves the known subcritical exponent α<23$\alpha <\frac{2}{3}$ under fluid‐free case.

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“…For instance, in two‐dimensional bounded domain, Espejo and Winkler [11] firstly studied global existence and stabilization of solutions for () with

S(n)=n

Section: Introductionmentioning

confidence: 99%

On a three‐dimensional chemotaxis‐Stokes system with nonlinear sensitivity modeling coral fertilization

Zheng

2022

Z Angew Math Mech

View full text Add to dashboard Cite

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Influence of Flux Limitation on Large Time Behavior in a Three-Dimensional Chemotaxis-Stokes System Modeling Coral Fertilization

Liu

2021

Acta Appl Math

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Large time behavior in a chemotaxis-Stokes system modeling coral fertilization with arbitrarily slow porous medium diffusion

Wang

2022

Journal of Mathematical Analysis and Applications

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Large time behavior in a three-dimensional degenerate chemotaxis-Stokes system modeling coral fertilization

Cited by 7 publications

References 48 publications

On a three‐dimensional chemotaxis‐Stokes system with nonlinear sensitivity modeling coral fertilization

On a three‐dimensional chemotaxis‐Stokes system with nonlinear sensitivity modeling coral fertilization

Influence of Flux Limitation on Large Time Behavior in a Three-Dimensional Chemotaxis-Stokes System Modeling Coral Fertilization

Large time behavior in a chemotaxis-Stokes system modeling coral fertilization with arbitrarily slow porous medium diffusion

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