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On blow-up for the hartree equation

WebTIME-DEPENDENT SCHRODINGER-HARTREE EQUATION Hristo Genev So a University St. Kl. Ohridski ... Nonlinear Schr odinger equation, solitary waves, blow-up solutions, variational methods. 903. Web01. dec 2024. · We study stable blow‐up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger‐type equation with a nonlocal, convolution‐type nonlinearity: First, we ...

Energy thresholds of blow‐up for the Hartree equation with a …

WebWe study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential [Formula: see text]. We establish the local well-posedness at the nonconserved critical regularity [Formula: see text] for [Formula: see text], which also includes the energy-supercritical regime [Formula: see text] (thus, … WebWe study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential i u t + Δ u + ( x − b ∗ u p) u p − 2 u = 0, x ∈ ℝ N.We establish the local well-posedness at the nonconserved critical regularity Ḣ s c for s c ≥ 0, which also includes the energy-supercritical regime s c > 1 (thus, complementing the … bhel market value https://lynnehuysamen.com

Stability of standing waves for the fractional Schrödinger–Hartree equation

Web03. apr 2013. · The purpose of this work is to identify a sharp criterion under which energy solutions of L 2 supercritical Hartree equation scatter. From the view of physical point, the criterion is represented in terms of the corresponding Lagrange functional and the virial quantity. This differs from Duyckaers et al. (Math Res Lett 15(6):1233–1250, 2008) … Web02. okt 2024. · In the intercritical setting the criterion produces blow-up solutions with the initial values above the mass-energy threshold. We conclude with examples showing currently known thresholds for global vs. finite time behavior. Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:1910.01085 [math.AP] (or arXiv:1910.01085v1 [math.AP] for … Web15. feb 2024. · Motivated by this problem, we study the scattering versus blow-up dichotomy of the solutions for the focusing L 2-supercritical, nonlinear, fractional Schrödinger equation (1.1). Similar to studies on the classical semi-linear Schrödinger equation (see [5] , [33] , [38] ), we attempt to use the variational method to find a sharp threshold of ... bhella cristy tiktok

[2206.12611] Local Uniqueness of blow-up solutions for critical Hartree …

Category:Sharp Threshold of Blow-up and Scattering for the fractional Hartree …

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On blow-up for the hartree equation

FOCUSING HARTREE EQUATION WITH INVERSE-SQUARE …

Web01. jul 2024. · Scattering versus blow-up for the focusing L 2 supercritical Hartree equation Z Angew Math Phy , 65 ( 2014 ) , pp. 179 - 202 CrossRef View in Scopus Google Scholar

On blow-up for the hartree equation

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Webmore information can be derived about the blow-up solutions and the ground state of (2) plays a crucial role in the study of the dynamics of the blow-up solutions. According to Theorem1.2, if k’k Web03. jun 2015. · On finite time blow-up for the mass-critical Hartree equations - Volume 145 Issue 3. ... Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms. Reviews in Mathematical Physics, Vol. 33, Issue. 09, p. 2150029. CrossRef;

WebON BLOW UP FOR A CLASS OF RADIAL HARTREE TYPE EQUATIONS SHUMAO WANG Abstract. We study a class of Hartree type equations and prove a quantitative blow up rate for their blow up solutions. This is an analogue of the result by Merle and Raphaël on 3d NLS. 1. INTRODUCTION We consider the Cauchy problem for the focusing … Web29. dec 2007. · Title: Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case. Authors: Changxing Miao, Guixiang Xu, Lifeng Zhao. Download a PDF of the paper titled Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case, by Changxing Miao ...

Web01. apr 2024. · Strong instability of standing waves for Hartree equation with harmonic potential. Physica D, 237 (2008), pp. 998-1005. View PDF View article View in Scopus Google Scholar [7] ... Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation. Dyn. Partial Differ. Equ., 7 (2) (2010), pp. 187-205. Web01. sep 2024. · The dynamics properties of blow-up solutions in L 2 and H s were investigated in [32], [42], [44], and the stability of equilibria was obtained in [6], [13], [14], [42] etc. Recently, the existence, uniqueness and regularity properties of local mild solutions for the space–time fractional Schrödinger equation with Hartree nonlinearity were ...

Web08. jun 2024. · On blow-up profile of ground states of boson stars with external potential. J. Stat. ... Yang, J.: Existence and mass concentration of pseudo-relativistic Hartree equation. J. Math. Phys. 58(8), 081501 (2024). 22 pp. Article MathSciNet Google Scholar Ye, H.: Mass minimizers and concentration for nonlinear Choquard equations in \({\mathbb ...

Web1 day ago · Big blow for Punjab Kings as Joshua Little removes Shikhar Dhawan for 8. Dhawan whips it over the mid-wicket as Alzarri Joseph takes a simple catch. Dhawan falls on a single digit for the first ... bhelma viWeb25. jun 2024. · Local Uniqueness of blow-up solutions for critical Hartree equations in bounded domain. Marco Squassina, Minbo Yang, Shunneng Zhao. In this paper we are interested in the following critical Hartree equation where , , is a small parameter, is a bounded domain in , and is the critical exponent in the sense of the Hardy-Littlewood … bhel vision mission valuesWeb01. jan 2010. · The new ingredient for the Hartree equation is the refi ned Gagliardo-Nirenberg inequality of the convo lution type (1.7), whose p roof is based on the well-known concentration compactness bheki kuneneWebThen at the minimal mass threshold, we can construct the finite-time blow up solution, which is a pseudo-conformal transformation of the ground state, up to the symmetries of the equation. Finally, we establish an mass concentration phenomenon of the finite-time blow up solution to the equation. bhelela pyei loginWeb15. feb 2024. · Motivated by this problem, we study the scattering versus blow-up dichotomy of the solutions for the focusing L 2-supercritical, nonlinear, fractional Schrödinger equation (1.1). Similar to studies on the classical semi-linear Schrödinger equation (see [5] , [33] , [38] ), we attempt to use the variational method to find a sharp threshold of ... bhelma iii la riojaWebON THE BLOW UP PHENOMENON FOR THE MASS CRITICAL FOCUSING HARTREE EQUATION WITH INVERSE-SQUARE POTENTIAL YU CHEN, CHAO LU, AND JING LU Abstract. In this paper, we consider the dynamics of the solution to the mass critical focusing Hartree equation with inverse-square potential in the energy space H1(Rd). The main … bhen ki laudiWeb01. jul 2024. · In this paper, we consider the complementary case M [u] 1-s c E [u] s c ≥ M [Q] 1-s c E [Q] s c and obtain a criteria on blow-up and global existence for the Hartree equation (0.1). Previous article in issue bhela kolkata