ترغب بنشر مسار تعليمي؟ اضغط هنا

Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion

253   0   0.0 ( 0 )
 نشر من قبل Hailong Ye
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we study the time periodic problem to a three-dimensional chemotaxis-Stokes model with porous medium diffusion $Delta n^m$ and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some iterative techniques, we obtain the existence and time-space uniform boundedness of weak time periodic solutions for any $m>1$. Moreover, we improve the regularity for $mlefrac{4}{3}$ and show that the obtained periodic solutions are in fact strong periodic solutions.



قيم البحث

اقرأ أيضاً

301 - Chunhua Jin 2021
In this paper, we study the consumption-chemotaxis-Stokes model with porous medium slow diffusion in a three dimensional bounded domain with zero-flux boundary conditions and no-slip boundary condition. In recent ten years, many efforts have been mad e to find the global bounded solutions of chemotaxis-Stokes system in three dimensional space. Although some important progress has been carried out in some papers, as mentioned by some authors, the question of identifying an optimal condition on m ensuring global boundedness in the three-dimensional framework remains an open challenge. In the present paper, we put forward a new estimation technique, completely proved the existence of global bounded solutions for arbitrary slow diffusion case, and partially answered the open problem proposed by Winkler.
71 - Weirun Tao , Yuxiang Li 2018
This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion begin{eqnarray} left{begin{array}{lll} n_t+ucdot abla n= ablacdot(| abla n|^{p-2} abla n)- ablacdot(nchi(c) abla c),& xinOmega, t>0, c_t+ucdot abla c=Delta c-nf(c),& xinOmega, t>0, u_t+(ucdot abla) u=Delta u+ abla P+n ablaPhi,& xinOmega, t>0, ablacdot u=0,& xinOmega, t>0 end{array}right. end{eqnarray} under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$ in a bounded convex domain $Omegasubset mathbb{R}^3$ with smooth boundary. Here, $Phiin W^{1,infty}(Omega)$, $0<chiin C^2([0,infty))$ and $0leq fin C^1([0,infty))$ with $f(0)=0$. It is proved that if $p>frac{32}{15}$ and under appropriate structural assumptions on $f$ and $chi$, for all sufficiently smooth initial data $(n_0,c_0,u_0)$ the model possesses at least one global weak solution.
61 - Ji Liu 2021
In this paper, we consider the following system $$left{begin{array}{ll} n_t+ucdot abla n&=Delta n- ablacdot(nmathcal{S}(| abla c|^2) abla c)-nm, c_t+ucdot abla c&=Delta c-c+m, m_t+ucdot abla m&=Delta m-mn, u_t&=Delta u+ abla P+(n+m) ablaPhi,qquad ab lacdot u=0 end{array}right.$$ which models the process of coral fertilization, in a smoothly three-dimensional bounded domain, where $mathcal{S}$ is a given function fulfilling $$|mathcal{S}(sigma)|leq K_{mathcal{S}}(1+sigma)^{-frac{theta}{2}},qquad sigmageq 0$$ with some $K_{mathcal{S}}>0.$ Based on conditional estimates of the quantity $c$ and the gradients thereof, a relatively compressed argument as compared to that proceeding in related precedents shows that if $$theta>0,$$ then for any initial data with proper regularity an associated initial-boundary problem under no-flux/no-flux/no-flux/Dirichlet boundary conditions admits a unique classical solution which is globally bounded, and which also enjoys the stabilization features in the sense that $$|n(cdot,t)-n_{infty}|_{L^{infty}(Omega)}+|c(cdot,t)-m_{infty}|_{W^{1,infty}(Omega)} +|m(cdot,t)-m_{infty}|_{W^{1,infty}(Omega)}+|u(cdot,t)|_{L^{infty}(Omega)}rightarrow0 quadtextrm{as}~trightarrow infty$$ with $n_{infty}:=frac{1}{|Omega|}left{int_{Omega}n_0-int_{Omega}m_0right}_{+}$ and $m_{infty}:=frac{1}{|Omega|}left{int_{Omega}m_0-int_{Omega}n_0right}_{+}.$
103 - Weirun Tao , Yuxiang Li 2018
This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion begin{equation} onumber left{ begin{aligned} &n_t+ucdot abla n= ablacdo tleft(| abla n|^{p-2} abla nright)- ablacdot(n abla c), &xinOmega, t>0, &c_t+ucdot abla c=Delta c-nc,&xinOmega, t>0, &u_t=Delta u+ abla P+n ablaphi ,&xinOmega, t>0, & ablacdot u=0, &xinOmega, t>0, end{aligned} right. end{equation} where $phiin W^{2,infty}(Omega)$ is the gravitational potential. It is proved that global bounded weak solutions exist whenever $p>frac{23}{11}$ and the initial data $(n_0,c_0,u_0)$ are sufficiently regular satisfying $n_0geq 0$ and $c_0geq 0$.
126 - Peter Y.H.Pang , Yifu Wang 2019
This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain $Omega subset mathbb{R}^N$ ($N=1,2$): $$label{0} left{begin{array}{ll} p_t=Delta p- ablacdotp p(displaystylefrac alpha {1+c} abla c+rho abla w)+lambda p(1-p),,& xin Omega, t>0, c_t=Delta c-c-mu pc,, &xin Omega, t>0, w_t= gamma p(1-w),,& xin Omega, t>0, end{array}right. $$ where $alpha, rho, lambda, mu$ and $gamma$ are positive parameters. For any reasonably regular initial data $(p_0, c_0, w_0)$, we prove the global boundedness ($L^infty$-norm) of $p$ via an iterative method. Furthermore, we investigate the long-time behavior of solutions to the above system under an additional mild condition, and improve previously known results. In particular, in the one-dimensional case, we show that the solution $(p,c,w)$ converges to $(1,0,1)$ with an explicit exponential rate as time tends to infinity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا