{"title":"OSCILLATIONS OF HIGHER-ORDER RETARDED DIFFERENTIAL EQUATIONS GENERATED BY THE RETARDED ARGUMENT","authors":"G. Ladas, V. Lakshmikantham, J. Papadakis","doi":"10.1016/B978-0-12-627250-5.50013-7","DOIUrl":"https://doi.org/10.1016/B978-0-12-627250-5.50013-7","url":null,"abstract":"","PeriodicalId":175822,"journal":{"name":"Functional differential equations","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116930465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Remarks on the Strong Solvability of the Navier-Stokes Equations","authors":"H. Amann","doi":"10.5167/UZH-21987","DOIUrl":"https://doi.org/10.5167/UZH-21987","url":null,"abstract":"Throughout this note m≥3 and either Ω=Rm, or Ω is a half-space of Rm, or Ω is a smooth domain in Rm with a compact boundary ∂Ω. We consider the following initial-boundary value problem (1) for the Navier-Stokes equations: \u0000∇⋅v∂tv+(v⋅∇)v−νΔvvv(⋅,0)=0=−∇p=0=v0in Ω,in Ω,on ∂Ω,in Ω. \u0000Of course, there is no boundary condition if Ω=Rm. \"In a recent paper [J. Math. Fluid Mech. 2 (2000), no. 1, 16--98] we investigated the strong solvability of (1) for initial data v0 belonging to certain spaces of distributions (modulo gradients). In this note we explain some of our main results in a very particular and simple setting. As usual, we concentrate on the velocity field v since the pressure field p is determined up to a constant by v.","PeriodicalId":175822,"journal":{"name":"Functional differential equations","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129436044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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