講座名稱：A 3D Keller-Segel-Navier-Stokes system involving subquadratic logistic degradation

講座人：向昭銀 教授

講座時(shí)間：11月12日10:00-11:00

地點(diǎn)：騰訊會(huì)議853-495-989

講座人介紹：

向昭銀，電子科技大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授、博士生導(dǎo)師。2006年博士研究生畢業(yè)于四川大學(xué)。從事偏微分方程的研究，在CPDE、CVPDE、IMRN、JFA、Math Z等國(guó)際知名期刊上發(fā)表學(xué)術(shù)論文70余篇，作為負(fù)責(zé)人主持多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目。入選四川省杰出青年學(xué)術(shù)技術(shù)帶頭人資助計(jì)劃、四川省學(xué)術(shù)和技術(shù)帶頭人后備人選等，曾獲四川省科學(xué)技術(shù)進(jìn)步獎(jiǎng)（自然科學(xué)類）二等獎(jiǎng)，四川省數(shù)學(xué)會(huì)基礎(chǔ)數(shù)學(xué)獎(jiǎng)一等獎(jiǎng)等獎(jiǎng)項(xiàng)。

講座內(nèi)容：

In this talk, we consider a Keller-Segel-Navier-Stokes system involving subquadratic logistic degradation in a three-dimensional smoothly bounded domain along with reasonably mild initial conditions and no- flux/no-flux/Dirichlet boundary conditions for cell population/ chemical/fluid.

The purpose of the present talk is to firstly show the generalized solvability for the model under some subquadratic logistic exponent restriction, which indicates that persistent Dirac-type singularities can be ruled out, and to secondly exhibit the eventual smoothness of these solutions under the stronger restriction whenever linear growth coefficient of population is not too large. These results especially extend the precedent works due to Winkler (J. Funct. Anal. 276 (2019): 1339-1401; Comm. Math. Phys. 367 (2022): 439-489.), where, among other things, the corresponding studies focus on the case of quadratic degradation. This is a joint work with Dr Yu TIAN.

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院