Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial data
نویسنده
چکیده
In this paper we prove that the cubic wave equation is globally well posed and scattering for radial initial data satisfying ‖|x|2ǫu0‖Ḣ1/2+ǫ(R3)+‖u0‖Ḣ1/2+ǫ(R3)+‖|x| 2ǫu1‖Ḣ−1/2+ǫ(R3)+‖u1‖Ḣ−1/2+ǫ(R3) < ∞. (0.1) This space of functions is slightly smaller than the general critical space, Ḣ× Ḣ.
منابع مشابه
Global Well-posedness for the Radial Defocusing Cubic Wave Equation on R and for Rough Data
We prove global well-posedness for the radial defocusing cubic wave equation
متن کاملGlobal Well-posedness for Solutions of Low Regularity to the Defocusing Cubic Wave Equation on R
We prove global well-posedness for the defocusing cubic wave equation
متن کاملAdapted Linear-nonlinear Decomposition and Global Well-posedness for Solutions to the Defocusing Cubic Wave Equation on R
We prove global well-posedness for the defocusing cubic wave equation
متن کاملGlobal Well-posedness and Scattering for Defocusing Energy-critical Nls in the Exterior of Balls with Radial Data
We consider the defocusing energy-critical NLS in the exterior of the unit ball in three dimensions. For the initial value problem with Dirichlet boundary condition we prove global well-posedness and scattering with large radial initial data in the Sobolev space Ḣ1 0 . We also point out that the same strategy can be used to treat the energy-supercritical NLS in the exterior of balls with Dirich...
متن کاملGlobal Well-posedness and Scattering for the Mass-critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions
We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation iut + ∆u = |u|4/nu for large spherically symmetric Lx(R n) initial data in dimensions n ≥ 3. After using the reductions in [32] to reduce to eliminating blowup solutions which are almost periodic modulo scaling, we obtain a frequency-localized Morawetz...
متن کامل