Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, \infty }(\mathbb {R}^d)$$

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2023-11-28 DOI:10.1007/s00028-023-00927-6

Hee Chul Pak

引用次数: 0

Abstract

An evidence of temporal discontinuity of the solution in $F^s_{1, \infty }(\mathbb {R}^d)$ is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.

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端点临界triiebel - lizorkin空间中不可压缩欧拉方程解的时间正则性 $$F^{d+1}_{1, \infty }(\mathbb {R}^d)$$

给出了$F^s_{1, \infty }(\mathbb {R}^d)$中解的时间不连续的证据，这暗示了欧拉方程的柯西问题的不适定性。讨论了相关空间中解的连续性和弱型连续性。

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

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators