Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

By Hao Jia, Vladimír Sverák. 2012

208 citations recorded by the source corpus.

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (−1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe328e9127c22f1c166f6ad538dd1b2af4171837

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jacob Bedrossian
2. Nader Masmoudi
3. Elia Brué
4. Dallas Albritton
5. Maria Colombo
6. Tai-Peng Tsai
7. Patrick Winkert
8. Giuseppe Mingione

In Control and Systems Engineering

1. Jacob Bedrossian
2. Elia Brué
3. Maria Colombo
4. Nader Masmoudi
5. Dallas Albritton
6. Tai-Peng Tsai
7. Pierre Germain

In Mathematical Physics

1. Jacob Bedrossian
2. Nader Masmoudi
3. Elia Brué
4. Maria Colombo
5. Dallas Albritton
6. Tai-Peng Tsai
7. Patrick Winkert
8. Leszek Gasinski

Citations in the corpus

• Non-uniqueness of Leray solutions of the forced Navier-Stokes equations (2021, background): “We mention two of particular importance: First, Jia, Šverák, and Guillod [32, 33, 28] developed a program towards non-uniqueness and supported the missing steps with numerical evidence.”
• Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$R2 with Measure-Valued Initial Data (2012, background): “In this general sense, the work here is related to the recent works on 3D NSE in the critical space L3,∞ [48, 47].”
• Forward Discretely Self-Similar Solutions of the Navier–Stokes Equations (2014, methodology): “In contrast, the solutions of [10] and [23] are constructed using the Leray–Schauder fixed point theorem for the equation for ṽ = v − ev0, namely, ṽ = K(ṽ) := T (F (ev0 + ṽ)), K : X → X, where T is essentially the Stokes solver, i.”
• Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, background): “In this general sense, the work here is related to the recent works on three dimensional NSE in the critical space L3,∞ [47,48].”