{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:15:59Z","timestamp":1758399359285,"version":"3.41.2"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871101"],"award-info":[{"award-number":["11871101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p>When we wanted to further investigate the results of Bourgain\u2013Pavlovi\u0107, Koch\u2013Tataru and Li\u2013Xiao\u2013Yang, we encountered the problem of stability of the parameter flow. For initial data in some space [Formula: see text], norm inflation implies that the solution does not belong to [Formula: see text]. For [Formula: see text], Auscher\u2013Dubois\u2013Tchamitchian proved that Koch\u2013Tataru\u2019s solution is stable in their defined space [Formula: see text]. In this paper, we consider Koch\u2013Tataru\u2019s iteration space and construct a non-Gauss flow function to show that [Formula: see text]-stability may have meaning different to [Formula: see text], which supports Chemin and Gallagher\u2019s point: well-posedness and norm inflation may have no conflict.<\/jats:p>","DOI":"10.1142\/s0219691323500030","type":"journal-article","created":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T03:21:40Z","timestamp":1672975300000},"source":"Crossref","is-referenced-by-count":2,"title":["Middle frequency band and remark on Koch\u2013Tataru\u2019s iteration space"],"prefix":"10.1142","volume":"21","author":[{"given":"Haibo","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. 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