A New Proof of the Existence of Suitable Weak Solutions and Other Remarks for the Navier-Stokes Equations

• 作者: Enrique Fernández-Cara Irene Marín-Gayte
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: NAVIER-STOKES Equations REGULARITY Caffarelli-Kohn-Nirenberg Estimates SEMI-IMPLICIT Euler Approximation Schemes
• 年，卷（期）: 2018,（4）
• 页码范围: 383-402
• 页数: 20页
• 分类号: O1

摘要

We prove that the limits of the semi-discrete and the discrete semi-implicit Euler schemes for the 3D Navier-Stokes equations supplemented with Dirichlet boundary conditions are suitable in the sense of Scheffer [1]. This provides a new proof of the existence of suitable weak solutions, first established by Caffarelli, Kohn and Nirenberg [2]. Our results are similar to the main result in [3]. We also present some additional remarks and open questions on suitable solutions.