The Baire category method for intermittent convex integration

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2023-10-31 DOI:10.1007/s10474-023-01380-0

G. Sattig, L. Székelyhidi

引用次数: 0

Abstract

We use a convex integration construction from [22] in a Baire category argument to show that weak solutions to the transport equation with incompressible vector fields with Sobolev regularity are generic in the Baire category sense. Using the construction of [7] we prove an analog statement for the 3D Navier–Stokes equations.

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间歇凸积分的Baire范畴法

在一个baircategory参数中，我们使用了[22]的凸积分构造，证明了具有Sobolev正则性的不可压缩矢量场内输运方程的弱解在Baire范畴意义上是一般的。利用[7]的构造，证明了三维Navier-Stokes方程的一个类比命题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.