Yi Chen, Yu Yan, Xiaoling Zhang
Abstract:
This article concerns the nonlinear Schrodinger equation (NLS) on
\(\mathbb{R}^3\) with subcubic and cubic nonlinearities.
For the cubic NLS, with initial data in \(H^m(\mathbb{R}^3)\),
we establish exponential growth of high-order Sobolev norms
by using modified energy functionals and lossless Strichartz estimates.
For the subcubic NLS, with data in \(H^2(\mathbb{R}^3)\), we establish polynomial
growth.
Submitted March 19, 2026. Published July 6, 2026.
Math Subject Classifications: 35Q55, 35B45
Key Words: Schrodinger equation; Sobolev norms; modified energy; Strichartz estimates.
DOI: 10.58997/ejde.2026.50
Show me the PDF file (365 KB), TEX file for this article.
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Yi Chen College of Mathematics, Hohai University Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems, Nanjing, China email: 241319010005@hhu.edu.cn |
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Yu Yan College of Mathematics, Hohai University Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems Nanjing, China email: 2413190010004@hhu.edu.cn |
| Xiaoling Zhang College of Mathematics, Hohai University Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems Nanjing, China email: xlzhang@hhu.edu.cn |
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