This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the ...This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.展开更多
We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R ...We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))).展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102, 11071177)
文摘This paper is concerned with the finite time blow-up phenomena for the vector nonlinear Schrdinger equations with a magnetic field which describe the spontaneous generation of a magnetic field in a cold plasma in the subsonic limit. After obtaining some a priori estimates,we prove under certain natural conditions that the solutions to the Cauchy problem of the vector nonlinear Schrdinger equations in two and three spatial dimensions blow up in a finite time. Assuming that a solution to the aforementioned vector nonlinear Schrdinger equations is radially symmetric with respect to spatial variables x,we show that if the initial energy is non-positive,then the solution blows up in three dimensions in a finite time.
基金the National Natural Science Foundation of China(11771314)the Sichuan Science and Technology Program(2022JDTD0019)the Guizhou Province Science and Technology Basic Project(Qian Ke He Basic[2020]1Y011)。
文摘We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))).
