Blowup for biharmonic nls
WebJul 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 ... WebNov 1, 2016 · For the blowup proof in R N, we derive a localized virial estimate for fractional NLS in R N, which uses Balakrishnan's formula for the fractional Laplacian (− Δ) s from …
Blowup for biharmonic nls
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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 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). …
WebThe 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. WebBlowup for Biharmonic NLS – arXiv Vanity Read this arXiv paper as a responsive web page with clickable citations. arXiv Vanityrenders academic papers from arXivas …
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 … 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 …
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...
WebJan 31, 2024 · Scattering for the non-radial inhomogenous biharmonic NLS equation. 14 June 2024. Luccas Campos & Carlos M. Guzmán. Scattering Theory for a Class of … flesh holesWebWe consider singular solutions of the L^2-critical biharmonic nonlinear Schrödinger equation. We 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 a … flesh highlighting powderWebIn 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 … flesh hole plugsWebSep 29, 2015 · Profile decompositions and Blowup phenomena of mass critical fractional Schr\"odinger equations. We study, under the radial symmetry assumption, the solutions to the fractional Schr\"odinger equations of critical nonlinearity in $\mathbb R^ {1+d}, d \geq 2$, with L\' {e}vy index $ {2d}/ ( {2d-1}) <…. Expand. chekouhow to clean your dishwasherfleshhoodWebsingular 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 ... chek parts limitedWebIn 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 … flesh hoodie