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

Vladimir Georgiev; Yuan Li

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

Graduate School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the half-wave equation iu_t = Du − |u|^{2 3}u in three dimension and in the mass critical. For initial data u(t₀,x) = u₀(x) ∈ H_rad¹/²(R³) with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate kD^{1 2}u(t)k₂ ∼ ^C(u0⁾ as t → 0⁻. |t|¹4

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 Sep 28

Keywords

Blow-up
Half-wave equation
Mass critical
Minimal mass

ASJC Scopus subject areas

General

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title = "Blowup dynamics for Mass Critical Half-wave equation in 3D",

abstract = "We consider the half-wave equation iut = Du − |u|2 3u in three dimension and in the mass critical. For initial data u(t0,x) = u0(x) ∈ Hrad1/2(R3) with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate kD1 2u(t)k2 ∼ C(u0) as t → 0−. |t|14",

keywords = "Blow-up, Half-wave equation, Mass critical, Minimal mass",

author = "Vladimir Georgiev and Yuan Li",

year = "2020",

month = sep,

day = "28",

language = "English",

journal = "Nuclear Physics A",

issn = "0375-9474",

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AU - Georgiev, Vladimir

AU - Li, Yuan

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N2 - We consider the half-wave equation iut = Du − |u|2 3u in three dimension and in the mass critical. For initial data u(t0,x) = u0(x) ∈ Hrad1/2(R3) with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate kD1 2u(t)k2 ∼ C(u0) as t → 0−. |t|14

AB - We consider the half-wave equation iut = Du − |u|2 3u in three dimension and in the mass critical. For initial data u(t0,x) = u0(x) ∈ Hrad1/2(R3) with radial symmetry, we construct a new class of minimal mass blowup solutions with the blow up rate kD1 2u(t)k2 ∼ C(u0) as t → 0−. |t|14

KW - Blow-up

KW - Half-wave equation

KW - Mass critical

KW - Minimal mass

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