2024 On blow-up for the hartree equation

On blow-up for the hartree equation

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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 ... WebWe study the blow-up of solutions to the focusing Hartree equation iut + ∆u+( x −γ ∗ u )u = 0. We use the strategy derived from the almost finite speed of propagation ideas devised by Bourgain (1999) and virial analysis to deduce that the solution with negative energy …

Scattering versus blow-up for the focusing L 2 supercritical Hartree ...

Web01. jan 2012. · Request PDF On blow-up for the Hartree equation We study the blow-up of solutions to the focusing Hartree equation iu t +Δu+( x -γ * u 2 )u=0. We use the strategy derived from the almost ... Web01. 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 cloud of goods new orleans

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

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) … Web24. maj 2024. · Qing Guo, Shihui Zhu. We consider the fractional Hartree equation in the -supercritical case, and we find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If and , then the solution is globally well-posed and scatters; if and , the solution blows up in finite time. This condition is sharp in the sense that the ... c-16x42g. teso 27.7

$Sharp threshold of blow-up and scattering for the fractional Hartree ...$

Well-posedness and blow-up properties for the generalized …

Web04. jan 2024. · This paper studies the blow-up solutions for the Schrödinger equation with a Hartree-type nonlinearity together with a power-type subcritical perturbation. The precisely sharp energy thresholds for blow-up and global existence are obtained by analyzing potential well structures for associated functionals. 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. c16th german soldiers helmetWeb15. 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 ... c16 timber 150 x 50

"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 … " - On blow-up for the hartree equation

On blow-up for the hartree equation

Nonlinear Hartree equation in high energy-mass - ScienceDirect

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 Web20. avg 2007. · We characterize the dynamics of the finite time blow up solutions with minimal mass for the focusing mass critical Hartree equation with $H^1(\mathbb{R}^4)$ data and ...

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Web13. apr 2024. · In this paper, we consider the pseudo-relativistic Hartree equation i∂tψ=− +m2ψ−1 x ∗ ψ 2ψonℝ3 and study travelling solitary waves of the form ψ(t, x) = eitμφ (x ... The explicit blow-up profile and rate will be computed. Volume 44, Issue 13. 15 September 2024. Pages 10403-10415. Related; Information; Close Figure Viewer. Web01. sep 2024. · Abstract. In this paper, we identify the sharp energy threshold for the global existence and blow-up to the Hartree equation with a focusing and defocusing perturbation, respectively, by utilizing ...

Web01. jul 2024. · This paper studies blow-up solutions for the inhomogeneous Schrödinger equation with L 2 supercritical nonlinearity. In terms of Strauss’ arguments in Strauss (1977) [22], we find a new compactness lemma for radial symmetric functions.Thus, we use it to derive the best constants of two generalized Gagliardo–Nirenberg type inequalities. 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

Web01. 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 WebThen 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.

Web01. 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

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 ... c16 timber joists pricesWeb01. apr 2024. · Using a Fourier spectral method, a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case is provided to study the possibility of finite time blow-up versus global existence, the nature of the blow- up, the stability and instability of nonlinear ground states and the … c16 timber postsWeb31. avg 2024. · Secondly, we analyse blow-up behaviours of maximal ground states $ \psi_\beta $ when $ \beta\rightarrow 0^+ $, and the optimal blow-up rate with respect to $ \beta $ will be calculated. Keywords: Semi-relativistic Hartree Equation , c16 timber prices ukWebWe 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, … c 16 cat truck engines for saleWeb25. 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 … c16 vs c24 woodWeb29. dec 2007. · DOI: 10.4064/cm114-2-5 Corpus ID: 6218942; Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case @article{Miao2007GlobalWS, title={Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case}, author={Changxing … c16 timber 100 x 50Web03. 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; c16x trencher specs