BLOW-UP SOLUTIONS OF TWO-COUPLED NONLINEAR SCHRODINGER EQUATIONS IN THE RADIAL CASE

We consider the blow-up solutions to the following coupled nonlinear Schrodinger equations {iu(t) + Delta u + (vertical bar u vertical bar(2p) + beta vertical bar u vertical bar(p-1) vertical bar v vertical bar(p+1))u = 0, iv(t) + Delta v + (vertical bar v vertical bar(2p) + beta vertical bar v vertical bar(p-1)vertical bar u vertical bar(p+1))v = 0, u(0, x) = u(0)(x), v(0, x) = v(0)(x), x is an element of R-N, t >= 0. 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 ((vertical bar x vertical bar u(0), vertical bar x vertical bar v(0)) is an element of L-2(R-N) x L-2 (R-N)).

Automated summary

In this study, we investigate the blow-up solutions of coupled nonlinear Schrodinger equations. By considering the conservation of mass and energy, we establish two sufficient conditions for the existence of radially symmetric blow-up solutions. Our results improve upon the previous study by Li and Wu [10], as we no longer assume finite variance.