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On Local Regularity of Distributional Solutions to the Navier--Stokes Equations

GiovanniP. Galdi

Abstract

We provide a sharp result that guarantees that a distributional solution satisfying the Prodi-Serrin condition is regular in the spatial variables. The solution does not need to belong to the (local) Leray-Hopf class.

On Local Regularity of Distributional Solutions to the Navier--Stokes Equations

Abstract

We provide a sharp result that guarantees that a distributional solution satisfying the Prodi-Serrin condition is regular in the spatial variables. The solution does not need to belong to the (local) Leray-Hopf class.
Paper Structure (3 sections, 6 theorems, 65 equations)

This paper contains 3 sections, 6 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Preparatory Results.
  3. Local Regularity

Key Result

Lemma 2.1

Theorems & Definitions (9)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Theorem 3.1
  • Remark 3.1
  • Remark 3.2
  • Remark 3.3
  • Lemma 3.1
  • Lemma 3.2