Blowup for biharmonic nls
WebOct 21, 2024 · DOI: 10.3934/DCDSB.2024156 Corpus ID: 224819864; Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient @article{Liu2024LocalWA, title={Local well-posedness and finite time blowup for fourth-order Schr{\"o}dinger equation with complex coefficient}, author={Xuan Liu and … Websingular 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 ...
Blowup for biharmonic nls
Did you know?
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... WebNov 21, 2024 · It is proved that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of $L^2$-norm, which is no less than the critical power, concentrates into the singularity. 35 PDF Some remarks on the inhomogeneous biharmonic NLS equation Carlos M. Guzm'an, A. Pastor Mathematics
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 … WebMay 17, 2024 · Blowup of cylindrically symmetric solutions for biharmonic NLS Tian-Xiang Gou Published 17 May 2024 Mathematics A BSTRACT . In this paper, we consider …
WebApr 4, 2024 · Blowup for Biharmonic NLS Article Full-text available Mar 2015 Enno Lenzmann Thomas Boulenger View Show abstract Dispersion estimates for fourth order Schrödinger equations Article Full-text... WebNov 17, 2015 · Later, Fibich et al. [10] carried out a rigorous survey to biharmonic NLS from mathematical point of views and proved global existence in time of solutions to the Cauchy problem for (1.1).
WebWe prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of L 2 -norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of …
WebJan 8, 2024 · A BSTRACT . In this paper, we consider blowup of solutions to the Cauchy problem for the following biharmonic NLS, , where d ≥ 1 , µ ∈ R and 0 < σ < ∞ if 1 ≤ d ≤ 4 and 0 < σ < 4 / ( d − 4) if d ... Blow-up of rough solutions to the fourth-order nonlinear Schrdinger equation. Shihui Zhu, Yang Han, Jian Zhang; Mathematics. 2011; 14 ... tiddy twisterWebThe 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. the mack richard pryorWebBlowup for Biharmonic NLS – arXiv Vanity Read this arXiv paper as a responsive web page with clickable citations. arXiv Vanityrenders academic papers from arXivas … the macksWebJan 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. the mack restaurant st louisthe mack showWebAug 7, 2024 · Blowup for Biharmonic NLS Thomas Boulenger, E. Lenzmann Mathematics 2015 We consider the Cauchy problem for the biharmonic (i.\,e.~fourth-order) NLS with focusing nonlinearity given by $i \partial_t u = \Delta^2 u - \mu \Delta u - u ^ {2 \sigma} u$ for $ (t,x) \in [0,T)… 56 PDF Nonlinear Schrödinger equations and sharp interpolation … tiddy st mawesWebIn the mass-critical case $\sigma=4/d$, we prove a general blowup result in finite or infinite time for radial data in $H^2 (\mathbb {R}^d)$. As a key ingredient, we utilize the time … the macks band