Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation

نویسنده

  • Ben Dodson
چکیده

We prove global well-posedness for the cubic, defocusing, nonlinear Schrödinger equation on R2 with data u0 ∈ H s(R2), s > 1/4. We accomplish this by improving the almost Morawetz estimates in [9].

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Almost Morawetz estimates and global well-posedness for the defocusing L-critical nonlinear Schrödinger equation in higher dimensions

In this paper, we consider the global well-posedness of the defocusing, L2 critical nonlinear Schrödinger equation in dimensions n ≥ 3. Using the I-method, we show the problem is globally well-posed in n = 3 when s > 25 , and when n ≥ 4, for s > n−2 n . We combine energy increments for the I-method, interaction Morawetz estimates, and almost Morawetz estimates to prove the result.

متن کامل

Bootstrapped Morawetz Estimates and Resonant Decomposition for Low Regularity Global Solutions of Cubic Nls on R

We prove global well-posedness for the L-critical cubic defocusing nonlinear Schrödinger equation on R with data u0 ∈ H(R) for s > 1 3 . The proof combines a priori Morawetz estimates obtained in [4] and the improved almost conservation law obtained in [6]. There are two technical difficulties. The first one is to estimate the variation of the improved almost conservation law on intervals given...

متن کامل

Global Existence and Scattering for Rough Solutions of a Nonlinear Schrödinger Equation on R

We prove global existence and scattering for the defocusing, cubic, nonlinear Schrödinger equation in Hs(R3) for s > 4 5 . The main new estimate in the argument is a Morawetz-type inequality for the solution φ. This estimate bounds ‖φ(x, t)‖ Lx,t (R 3×R) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls ∫ ∞

متن کامل

M ar 2 00 7 IMPROVED INTERACTION MORAWETZ INEQUALITIES FOR THE CUBIC NONLINEAR SCHRÖDINGER EQUATION ON

We prove global well-posedness for low regularity data for the L 2 − critical defocusing nonlinear Schrödinger equation (NLS) in 2d. More precisely we show that a global solution exists for initial data in the Sobolev space H s (R 2) and any s > 2 5. This improves the previous result of Fang and Grillakis where global well-posedness was established for any s ≥ 1 2. We use the I-method to take a...

متن کامل

Almost Conservation Laws and Global Rough Solutions to a Nonlinear Schrödinger Equation

We prove an “almost conservation law” to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H(R) when n = 2, 3 and s > 4 7 , 5 6 , respectively.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009