{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T22:39:31Z","timestamp":1649025571839},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,3,25]],"date-time":"2009-03-25T00:00:00Z","timestamp":1237939200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>The main goal of this paper is to obtain the lower bounds<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0308210507000133_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>for solutions <jats:italic>u<\/jats:italic><jats:sub>\u03bd<\/jats:sub> of nonlinear Schr\u00f6dinger equations with small viscosity \u03bd. We also discuss the application of the above estimate to the theory of turbulence. Namely, we are interested in time-averaged lower bounds, which are important in establishing upper bounds for the turbulent space-scale.<\/jats:p>","DOI":"10.1017\/s0308210507000133","type":"journal-article","created":{"date-parts":[[2009,3,25]],"date-time":"2009-03-25T10:50:36Z","timestamp":1237978236000},"page":"237-251","source":"Crossref","is-referenced-by-count":1,"title":["Lower bounds for derivatives of solutions for nonlinear Schr\u00f6dinger equations"],"prefix":"10.1017","volume":"139","author":[{"given":"Andrei","family":"Biryuk","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,25]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210507000133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T15:08:48Z","timestamp":1556636928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210507000133\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,25]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0308210507000133"],"URL":"https:\/\/doi.org\/10.1017\/s0308210507000133","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,25]]}}}