Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℳ
-
George Venkov
gvenkov@tu-sofia.bg
Downloads
Abstract
The main purpose of the present paper is to consider the well-posedness of the L2-critical nonlinear Schrödinger equation of a Hartree type
ð’¾âˆ‚tψ + △ψ = (|x|−1 ∗ |ψ|8/3)ψ, (t, x) ∈ â„+ × â„3.
More precisely, we shall establish the local existence of solutions for initial data ψ0 in L2(â„3), as well as the existence of global solutions for small initial data. Moreover, we shall prove the existence of scattering operator.
Keywords
Similar Articles
- Ghislain R. Franssens, On the impossibility of the convolution of distributions , CUBO, A Mathematical Journal: Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal
- Sorin G. Gal, Remarks on the generation of semigroups of nonlinear operators on p-Fréchet spaces, 0 < p < 1 , CUBO, A Mathematical Journal: Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal
- Vediyappan Govindan, Choonkil Park, Sandra Pinelas, Themistocles M. Rassias, Hyers-Ulam stability of an additive-quadratic functional equation , CUBO, A Mathematical Journal: Vol. 22 No. 2 (2020)
- Stephen McDowall, Optical Tomography for Media with Variable Index of Refraction , CUBO, A Mathematical Journal: Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal
- Jyotirmoy Mouley, M. M. Panja, B. N. Mandal, Approximate solution of Abel integral equation in Daubechies wavelet basis , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- Peter D. Hislop, Fundamentals of scattering theory and resonances in quantum mechanics , CUBO, A Mathematical Journal: Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal
- Ruchi Arora, Dharmendra Kumar, Ishita Jhamb, Avina Kaur Narang, Mathematical Modeling of Chikungunya Dynamics: Stability and Simulation , CUBO, A Mathematical Journal: Vol. 22 No. 2 (2020)
- Abdeldjalil Aouane, Smaïl Djebali, Mohamed Aziz Taoudi, Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions , CUBO, A Mathematical Journal: Vol. 22 No. 3 (2020)
- Augustin Banyaga, Symplectic geometry and related structures , CUBO, A Mathematical Journal: Vol. 6 No. 1 (2004): CUBO, A Mathematical Journal
- Filippo Cammaroto, Infinitely many solutions for a nonlinear Navier problem involving the \(p\)-biharmonic operator , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
<< < 2 3 4 5 6 7 8 9 10 11 12 13 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
Published
2009-09-01
How to Cite
[1]
G. Venkov, “Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℳ”, CUBO, vol. 11, no. 4, pp. 15–28, Sep. 2009.
Issue
Section
Articles
