Blowup dynamics for Mass Critical Half-wave equation in 3D

Abstract

We consider the half-wave equation $i{u}_t=Du-|u{|}^{\frac{2}{3}}u$ in three dimension and in the mass critical. For initial data $u(t_0,x)=u_0(x)\in H_{rad}^{1/2}({\mathbb{R}}^3)$ with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate $\Vert D^{\frac{1}{2}}u(t){\Vert }_2\sim \frac{C(u_0)}{|t{|}^{\frac{1}{4}}}$ as $t\to 0^{-}$.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2007.15370

References in corpus (12)

• Uniqueness and Nondegeneracy of Ground States for $(-\Delta {)}^{s}Q+Q-Q^{\alpha +1}=0$ in $\mathbb{R}$
• Boson Stars as Solitary Waves
• On the continuum limit for discrete NLS with long-range lattice interactions
• Numerical study of fractional Nonlinear Schrödinger equations
• Nondispersive solutions to the L2-critical half-wave equation
• High speed excited multi-solitons in nonlinear Schrödinger equations
• On collapsing ring blow up solutions to the mass supercritical NLS
• On Traveling Solitary Waves and Absence of Small Data Scattering for Nonlinear Half-Wave Equations
• Two soliton solutions to the three dimensional gravitational Hartree equation
• Traveling waves for the quartic focusing Half Wave equation in one space dimension
• On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation
• Nondispersive solutions to the mass critical half-wave equation in two dimensions