Large global solutions for nonlinear Schrodinger equations I, mass-subcritical cases

作者：Beceanu, Marius; Deng, Qingquan; Soffer, Avy; Wu, Yifei^*

来源：Advances in Mathematics, 2021, 391: 107973.

DOI：10.1016/j.aim.2021.107973

• Nonlinear Schrodinger equation
• Global well-posedness
• Critical regularity

In this paper, we consider the nonlinear Schrodinger equation, @@@ i partial derivative(t)u + Delta u = mu vertical bar u vertical bar(p)u, (t, x) is an element of Rd+1, @@@ with mu= +/- 1, p > 0. @@@ In this work, we consider the mass-subcritical cases, that is, p is an element of (0, 4/d). We prove that under some restrictions on d, p, any radial initial data in the critical space H-sc (R-d) with compact support, implies global well-posedness.

• 单位
  天津大学