{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T00:31:02Z","timestamp":1761093062175,"version":"build-2065373602"},"reference-count":40,"publisher":"IOP Publishing","issue":"10","license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["2020\/00162\/CEECIND"],"award-info":[{"award-number":["2020\/00162\/CEECIND"]}]},{"DOI":"10.13039\/501100004155","name":"Magnus Ehrnroothin S\u00e4\u00e4ti\u00f6","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004155","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2025,10,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schr\u00f6dinger equation in infinite time in dimension <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>N<\/mml:mi>\n                           <mml:mtext>\u2a7e<\/mml:mtext>\n                           <mml:mn>13<\/mml:mn>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula>. Our solution is radially symmetric and converges asymptotically to the sum of two bubbles. The scale of one of the bubble is of order 1 whereas the other one is of order <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mo stretchy=\"false\">|<\/mml:mo>\n                           <mml:mi>t<\/mml:mi>\n                           <mml:msup>\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                              <mml:mrow>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mfrac>\n                                    <mml:mn>2<\/mml:mn>\n                                    <mml:mrow>\n                                       <mml:mi>N<\/mml:mi>\n                                       <mml:mo>\u2212<\/mml:mo>\n                                       <mml:mn>12<\/mml:mn>\n                                    <\/mml:mrow>\n                                 <\/mml:mfrac>\n                              <\/mml:mrow>\n                           <\/mml:msup>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula>. Moreover, the phase between the two bubbles form a right angle.<\/jats:p>","DOI":"10.1088\/1361-6544\/ae117d","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T10:02:03Z","timestamp":1761040923000},"page":"105013","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Construction of 2-bubbles for the energy critical bi-harmonic Schr\u00f6dinger equation"],"prefix":"10.1088","volume":"38","author":[{"given":"Jean-Baptiste","family":"Casteras","sequence":"first","affiliation":[]},{"given":"Ilkka","family":"Holopainen","sequence":"additional","affiliation":[]},{"given":"L\u00e9onard","family":"Monsaingeon","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"key":"nonae117dbib1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0764-4442(00)00120-8","type":"journal-article","article-title":"Dispersion estimates for fourth order Schr\u00f6dinger equations","volume":"330","author":"Ben-Artzi","year":"2000","journal-title":"C. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2025-01-31","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-10-09","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-10-21","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}