In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator...In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 0<s<1,N>2s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.展开更多
In this paper, a new operator splitting scheme is introduced for the numerical solution of the incompressible Navier-Stokes equations. Under some mild regularity assumptions on the PDE solution, the stability of the s...In this paper, a new operator splitting scheme is introduced for the numerical solution of the incompressible Navier-Stokes equations. Under some mild regularity assumptions on the PDE solution, the stability of the scheme is presented, and error estimates for the velocity and the pressure of the proposed operator splitting scheme are given.展开更多
基金supported in part by the NationalNatural Science Foundation of China(11801153,11501403,11701322,11561072)the Honghe University Doctoral Research Programs(XJ17B11,XJ17B12,DCXL171027,201810687010)+4 种基金the Yunnan Province Applied Basic Research for Youths(2018FD085)the Yunnan Province Local University(Part)Basic Research Joint Project(2017FH001-013)the Natural Sciences Foundation of Yunnan Province(2016FB011)the Yunnan Province Applied Basic Research for General Project(2019FB001)Technology Innovation Team of University in Yunnan Province。
文摘In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 0<s<1,N>2s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.
文摘In this paper, a new operator splitting scheme is introduced for the numerical solution of the incompressible Navier-Stokes equations. Under some mild regularity assumptions on the PDE solution, the stability of the scheme is presented, and error estimates for the velocity and the pressure of the proposed operator splitting scheme are given.
