{"title":"用爆破法估计涡度内迹和高导数估计","authors":"Jincheng Yang","doi":"10.1016/j.jde.2025.113486","DOIUrl":null,"url":null,"abstract":"<div><div>We derive several nonlinear a priori trace estimates for the 3D incompressible Navier–Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blow-up method and a novel averaging operator, which could apply to PDEs with scaling invariance and <em>ε</em>-regularity, possibly with a drift.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113486"},"PeriodicalIF":2.3000,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Vorticity interior trace estimates and higher derivative estimates via blow-up method\",\"authors\":\"Jincheng Yang\",\"doi\":\"10.1016/j.jde.2025.113486\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We derive several nonlinear a priori trace estimates for the 3D incompressible Navier–Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blow-up method and a novel averaging operator, which could apply to PDEs with scaling invariance and <em>ε</em>-regularity, possibly with a drift.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"442 \",\"pages\":\"Article 113486\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2025-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039625005133\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625005133","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Vorticity interior trace estimates and higher derivative estimates via blow-up method
We derive several nonlinear a priori trace estimates for the 3D incompressible Navier–Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blow-up method and a novel averaging operator, which could apply to PDEs with scaling invariance and ε-regularity, possibly with a drift.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics