DYNAMICAL PROPERTIES OF BLOW-UP SOLUTIONS FOR THE GROSS-PITAEVSKII-POISSON EQUATION

DYNAMICAL PROPERTIES OF BLOW-UP SOLUTIONS FOR THE GROSS-PITAEVSKII-POISSON EQUATION | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 13 December 2025 V1 Latest version Share on DYNAMICAL PROPERTIES OF BLOW-UP SOLUTIONS FOR THE GROSS-PITAEVSKII-POISSON EQUATION Authors : LI XIONG and WANG SHENG [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176561838.89916718/v1 144 views 108 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper concerns the dynamical properties of blow-up solutions for the two-dimensional (2D) Gross-Pitaevskii-Poisson equation modelling dipolar Bose-Einstein condensates. Specifically, by virtue of the sharp Gagliardo-Nirenberg inequality and the variational characterization of the ground state for the classic nonlinear Schrödinger equation, we prove that the solution u ( t ) has no L 2 -limit as t → T ∗, provided that u ( t ) blows up in the norm ∥ · ∥ Σ at time T ∗ . Furthermore, in the special case where the initial datum u 0 is radially symmetric, we demonstrate the concentration phenomenon of blow-up solutions at the origin. Supplementary Material File (gpp_12.11.pdf) Download 125.47 KB Information & Authors Information Version history V1 Version 1 13 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords blow-up solution concentration gross-pitaevskii-poisson equations Authors Affiliations LI XIONG Sichuan Normal University View all articles by this author WANG SHENG [email protected] Sichuan Normal University View all articles by this author Metrics & Citations Metrics Article Usage 144 views 108 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation LI XIONG, WANG SHENG. DYNAMICAL PROPERTIES OF BLOW-UP SOLUTIONS FOR THE GROSS-PITAEVSKII-POISSON EQUATION. Authorea . 13 December 2025. DOI: https://doi.org/10.22541/au.176561838.89916718/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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