考虑了R^n上n(n≥2)维向列型液晶流(u,d)当初值属于Q_α^(-1)(R^n,R^n)×Q_α(R^n,S^2)(其中α∈(0,1))时Cauchy问题的适定性,这里的Q_α(R^n)最早由Essen,Janson,Peng和Xiao(见[Essen M,Janson S,Peng L,Xiao J.Q space of several...考虑了R^n上n(n≥2)维向列型液晶流(u,d)当初值属于Q_α^(-1)(R^n,R^n)×Q_α(R^n,S^2)(其中α∈(0,1))时Cauchy问题的适定性,这里的Q_α(R^n)最早由Essen,Janson,Peng和Xiao(见[Essen M,Janson S,Peng L,Xiao J.Q space of several real variables,Indiana Univ Math J,2000,49:575-615])引入,是指由R^n中满足的所有可测函数f全体所组成的空间.上式左端在取遍Rn中所有以l(I)为边长且边平行于坐标轴的立方体I的全体中取上确界,而Q_α^(-1)(R^n):=▽·Q_α(R^n).最后证明了解(u,d)在类C([0,T);Q_(α,T)^(-1)(R^n,R^n))∩L_(loc)~∞((0,T);L~∞(R^n,R^n))×C([0,T);Q_α,T(R^n,S^2))∩L_(loc)~∞((0,T);W^(1,∞)(R^n,S^2))(其中0<T≤∞)中是唯一的.展开更多
文摘考虑了R^n上n(n≥2)维向列型液晶流(u,d)当初值属于Q_α^(-1)(R^n,R^n)×Q_α(R^n,S^2)(其中α∈(0,1))时Cauchy问题的适定性,这里的Q_α(R^n)最早由Essen,Janson,Peng和Xiao(见[Essen M,Janson S,Peng L,Xiao J.Q space of several real variables,Indiana Univ Math J,2000,49:575-615])引入,是指由R^n中满足的所有可测函数f全体所组成的空间.上式左端在取遍Rn中所有以l(I)为边长且边平行于坐标轴的立方体I的全体中取上确界,而Q_α^(-1)(R^n):=▽·Q_α(R^n).最后证明了解(u,d)在类C([0,T);Q_(α,T)^(-1)(R^n,R^n))∩L_(loc)~∞((0,T);L~∞(R^n,R^n))×C([0,T);Q_α,T(R^n,S^2))∩L_(loc)~∞((0,T);W^(1,∞)(R^n,S^2))(其中0<T≤∞)中是唯一的.
