Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space 𝑊^{𝑠,𝑝} for 𝑝<2

Type: Article

Publication Date: 2010-04-20

Citations: 19

DOI: https://doi.org/10.1090/s0002-9947-10-05055-5

Locations

  • Transactions of the American Mathematical Society - View

Similar Works

Action Title Year Authors
+ Cauchy problem of nonlinear Schr\"odinger equation with Cauchy problem of nonlinear Schr\"odinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$ 2007 Yi Zhou
+ Cauchy problem of nonlinear Schrödinger equation with Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$ 2007 Yi Zhou
+ Cauchy problem of nonlinear Schrödinger equation with Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p&lt;2$ 2007 Yi Zhou
+ PDF Chat Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in $H^{s} (\mathbb R^{n})$ 2021 JinMyong An
JinMyong Kim
KyuSong Chae
+ Global existence for Schrödinger–Debye system for initial data with infinite 𝐿²-norm 2015 Adán J. Corcho
Lucas C. F. Ferreira
+ Cauchy problem for a nonlinear Schrödinger equation with a large initial gradient in the weakly dispersive limit 2024 Sergei V. Zakharov
+ PDF Chat The Sobolev-Morawetz approach for the energy scattering of nonlinear Schrödinger-type equations with radial data 2020 Van Duong Dinh
Sahbi Keraani
+ PDF Chat Schrödinger equations: pointwise convergence to the initial data 1988 Luis Vega
+ Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with initial potential in weighted sobolev space 2021 Meisen Chen
Engui Fan
+ Разрушение решений задачи Коши для нелинейного уравнений Шредингера 2013 В. Ж. Сакбаев
+ The Cauchy Problem of the Nonlinear Schrodinger Equations in R^1+1 2007 Guixiang
Xu Xu
+ Nonlinear Schrödinger equation on the half-line with nonlinear boundary condition 2015 Ahmet Batal
Türker Özsarı
+ Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions 2016 Ahmet Batal
Türker Özsarı
+ PDF Chat The Cauchy problem for 𝑢_{𝑡}=Δ𝑢^{𝑚} when 0&lt;𝑚&lt;1 1985 Miguel A. Herrero
Michel Pierre
+ PDF Chat Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data 2021 Shaoming Guo
Xianfeng Ren
Baoxiang Wang
+ Global existence and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential 2022 JinMyong An
RoeSong Jang
Jinmyong Kim
+ Long-time asymptotic behavior of the modified Schrödinger equation via ∂¯-steepest descent method 2021 Yiling Yang
Engui Fan
+ PDF Chat Sharp condition of global well-posedness for inhomogeneous nonlinear Schrödinger equation 2021 Chao Yang
+ Continuous dependence of Cauchy problem for nonlinear Schrödinger equation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup></mml:math> 2013 Wei Dai
Weihua Yang
Daomin Cao
+ PDF Chat $ H^2 $ blowup result for a Schrödinger equation with nonlinear source term 2020 Xuan Liu
Ting Zhang

Works That Cite This (19)

Action Title Year Authors
+ An Lp-theory for almost sure local well-posedness of the nonlinear Schrödinger equations 2018 Oana Pocovnicu
Yuzhao Wang
+ PDF Chat Estimates on the modulation spaces for the Dirac equation with potential 2018 Keiichi Kato
Ivan Naumkin
+ Higher-order nonlinear Schrödinger equations with singular data 2017 Nakao Hayashi
Pavel I. Naumkin
Takayoshi Ogawa
+ Nonlinear Schrödinger systems in 2d with nondecaying final data 2015 Nakao Hayashi
Chunhua Li
Pavel I. Naumkin
+ The Hartree and Hartree–Fock Equations in Lebesgue $$L^p$$ and Fourier–Lebesgue $$\widehat{L}^p$$ Spaces 2022 Divyang G. Bhimani
Saikatul Haque
+ Local and global well-posedness, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:math>-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in L 2020 Ryosuke Hyakuna
+ Critical nonlinear Schrödinger equations with data in homogeneous weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="bold">L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> spaces 2014 Chunhua Li
Nakao Hayashi
+ Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability 2017 Gaku Hoshino
Ryosuke Hyakuna
+ PDF Chat On existence of global solutions of Schrödinger equations with subcritical nonlinearity for $̂L^{p}$-initial data 2012 Ryosuke Hyakuna
Masayoshi Tsutsumi
+ PDF Chat Global well-posedness for the fourth-order Hartree-type Schrödinger equation with Cauchy data in $ L^{p} $ 2023 Jin Xie
Wang Deng
Han Yang