Blowup for biharmonic nls
WebDec 1, 2011 · This paper is concerned with the Cauchy problem for the biharmonic nonlinear Schrödinger equation with L2L2-super-critical nonlinearity. By establishing the profile decomposition of bounded... WebIn the mass-critical case a = 4/d, we prove a general blowup result in finite or infinite time for radial data in H-2 (R-d). As a key ingredient, we utilize the time evolution of a …
Blowup for biharmonic nls
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WebFeb 19, 2024 · Our findings appear to be the first rigorous results on upper bounds and existence of blowup solutions for biharmonic NLS. As a key ingredient, we utilize the … WebBLOWUP FOR BIHARMONIC NLS by Thomas BOULENGER and Enno LENZMANN Abstract. — We consider the Cauchy problem for the biharmonic (i.e., fourth-order) NLS with focusing nonlinearity given by i@tuD†2u †ujuj2˙u for .t;x/2„0;T/ Rd; where 0<˙<1for d 6 4and 0<˙6 4=.d 4/for d > 5; and 2R is some parameter to include a possible lower-order ...
Blowup for Biharmonic NLS Thomas Boulenger, Enno Lenzmann We consider the Cauchy problem for the biharmonic (i.\,e.~fourth-order) NLS with focusing nonlinearity given by for , where for and for ; and is some parameter to include a possible lower-order dispersion. WebJan 12, 2024 · Using the Morawetz estimates, Feng, the second and third authors [10] considered the small potential V when N ≥ 7 for the defocusing BNLS V (1.1) with non-radial initial data.
WebJan 13, 2024 · Blow-up solutions of the intercritical inhomogeneous NLS equation: the non-radial case Mykael Cardoso, L. Farah Materials Science Mathematische Zeitschrift 2024 In this paper we consider the inhomogeneous nonlinear Schrödinger (INLS) equation i∂tu+Δu+ x -b u 2σu=0,x∈RN\documentclass [12pt] {minimal} \usepackage {amsmath} … Webexistence of blowup solutions for radial data in H2pRdq satisfying criteria that appear natural from known results on blowup for NLS and nonlinear wave equations (NLW). …
WebMar 20, 2024 · Our findings appear to be the first rigorous results on upper bounds and existence of blowup solutions for biharmonic NLS. As a key ingredient, we utilize the time evolution of a nonnegative ...
WebMar 5, 2015 · Blowup for Biharmonic NLS. We consider the Cauchy problem for the biharmonic (i.\,e.~fourth-order) NLS with focusing nonlinearity given by $i … lyreco toneryWebAug 1, 2009 · Our findings appear to be the first rigorous results on upper bounds and existence of blowup solutions for biharmonic NLS. As a key ingredient, we utilize the time evolution of a nonnegative ... lyreco toolbox italiaWebMay 17, 2024 · In the mass critical and supercritical cases, we establish the existence of blowup solutions to the problem for cylindrically symmetric data. Our result extends the … lyreco torchWebJul 2, 2013 · The study of biharmonic (fourth-order) nonlinear Schrödinger equations (NLS) has attracted a significant amount of attention in the recent past; see e. g. [17,1,12,19,20, 21, 6,3,5,4,10]. The ... lyreco toilet rollsWebThis extends the first rigorous results on blowing-up solutions for the biharmonic NLS due to Boulenger and Lenzmann [9] and confirm numerical conjectures from [1, 2, 3, 11]. Normalized... lyreco tonerWebsingular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a ... than that for the critical NLS. Indeed, a rigorous proof of the blowup rate and blowup profile of the supercritical NLS was obtained very recently, and only in the ... lyreco toolsWebThe role of small fourth-order dispersion has been considered in a series of papers by Karpman and Shagalov (see [21] and the references therein), who studied the equation (3) iψt (t, x) + ∆ψ + ψ 2σ ψ + u000f∆2 ψ = 0 in the case when u000f < 0, where ∆2 is the biharmonic operator. lyreco tork h1