In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if ku0k 1nL1 ku0k1−1n L...In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if ku0k 1nL1 ku0k1−1n L∞andκk∇v0kLp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass ku0kL1 is large.Moreover,the decay rates of the classical solution are also obtained.展开更多
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>展开更多
为了对二维流体耦合Patlak-Keller-Segel-Naiver-Stokes趋化模型的全局适定性进行研究,建立了一些具有单调性的不等式并利用Gronwall不等式、插值不等式、Holder不等式等,得到当细胞初始质量M=∫R 2 n 0(x)d x≤8π时,该系统具有全局存...为了对二维流体耦合Patlak-Keller-Segel-Naiver-Stokes趋化模型的全局适定性进行研究,建立了一些具有单调性的不等式并利用Gronwall不等式、插值不等式、Holder不等式等,得到当细胞初始质量M=∫R 2 n 0(x)d x≤8π时,该系统具有全局存在的温和解.展开更多
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20160856)the National Natural Science Foundation of China(11801137)。
文摘In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if ku0k 1nL1 ku0k1−1n L∞andκk∇v0kLp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass ku0kL1 is large.Moreover,the decay rates of the classical solution are also obtained.
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>
