Global dynamics above the ground state energy for the 3D Zakharov system

[2608.14993] Global dynamics above the ground state energy for the 3D Zakharov system Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2608.14993 (math) [Submitted on 15 Aug 2026] Title: Global dynamics above the ground state energy for the 3D Zakharov system Authors: Zihua Guo , Kenji Nakanishi View a PDF of the paper titled Global dynamics above the ground state energy for the 3D Zakharov system, by Zihua Guo and Kenji Nakanishi View PDF HTML (experimental) Abstract: We study the global dynamics for the 3D Zakharov system with radial initial data of energy slightly above the ground state energy, proving that the initial data set splits into nine nonempty, pairwise disjoint regions in which the solutions have distinct behaviors: growup, scattering, or trapped by the ground state, as time goes in the forward or backward directions. It is a classification similar to those for the nonlinear Klein-Gordon equation and for the nonlinear Schrödinger equation, extending the previous results on the Zakharov system below the ground state energy. The proof relies on the normal form technique to handle the quadratic frequency interactions and careful modulational analysis around the ground state. One novelty is a new family of localized virial estimates with monotonicity. These virial estimates are crucial for us to study the dynamics away from the ground state and may be of independent interest for other purposes. Comments: 48 pages Subjects: Analysis of PDEs (math.AP) MSC classes: 35Q55, 35L52, 37K40 Cite as: arXiv:2608.14993 [math.AP] (or arXiv:2608.14993v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2608.14993 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kenji Nakanishi [ view email ] [v1] Sat, 15 Aug 2026 02:46:32 UTC (54 KB) Full-text links: Access Paper: View a PDF of the paper titled Global dynamics above the ground state energy for the 3D Zakharov system, by Zihua Guo and Kenji Nakanishi View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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