94 citations · 118 across the 7 of their papers we have counts for
7 papers
An interpolation inequality and its application in Keller-Segel model
Xinru Cao
In this paper, we first prove an interpolation inequality of Ehrling-type, which is an improvement of a special case to the well known Gargliardo-Nirenberg inequality. Then we appl…
Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics
Xinru Cao, Shunsuke Kurima, Masaaki Mizukami
This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =Δn_1 - χ_1\nabla\cdot(n_1\nabla c)+ μ_1n_1(1- n_1 - a_1n_2)…
Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term
Xinru Cao
The coupled chemotaxis fluid system \begin{equation} \left\{ \begin{array}{llc} \displaystyle n_t=Δn-\nabla\cdot(nS(x,n,c)\cdot\nabla c)-u\cdot\nabla n, &(x,t)\in Ω\times (0,T),\\…
Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities
Xinru Cao, Johannes Lankeit
The coupled chemotaxis fluid system \begin{equation} \left\{ \begin{array}{llc} n_t=Δn-\nabla\cdot(n S(x,n,c)\cdot\nabla c)-u\cdot\nabla n, &(x,t)\in Ω\times (0,T), \displaystyle c…
Boundedness in a quasilinear fully parabolic Keller-Segel system of higher dimension with logistic source
Cibing Yang, Xinru Cao, Zhaoxin Jiang +1
This paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of logistic type $ u_t=\nabla\cdot(ϕ(u)\nabla u)-χ\nabla\cdot…
Boundedness in a three-dimensional chemotaxis-haptotaxis model
Xinru Cao
This paper studies the chemotaxis-haptotaxis system \begin{equation}\nonumber \left\{ \begin{array}{llc} u_t=Δu-χ\nabla\cdot(u\nabla v)-ξ\nabla\cdot(u\nabla w)+μu(1-u-w), &(x,t)\in…
Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
Xinru Cao
In this paper, the fully parabolic Keller-Segel system \begin{equation} \left\{ \begin{array}{llc} u_t=Δu-\nabla\cdot(u\nabla v), &(x,t)\in Ω\times (0,T),\\ v_t=Δv-v+u, &(x,t)\inΩ\…