Discretely self-similar solutions to the Navier-Stokes equations with data in \(L_{\text{loc}}^2\) satisfying the local energy inequality

DOI10.2140/apde.2019.12.1943zbMath1431.35100arXiv1801.08060OpenAlexW3100921122WikidataQ126976630 ScholiaQ126976630MaRDI QIDQ2279785

Zachary Bradshaw, Tai-Peng Tsai

Publication date: 13 December 2019

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.08060

zbMATH Keywords

weak solutionNavier-Stokes equationsself-similar solution

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Weak solutions to PDEs (35D30) Self-similar solutions to PDEs (35C06)

Related Items (11)

Global weak solutions of the Navier-Stokes equations for intermittent initial data in half-space ⋮ Existence of global weak solutions to the Navier-Stokes equations in weighted spaces ⋮ Regular sets and an \(\varepsilon \)-regularity theorem in terms of initial data for the Navier-Stokes equations ⋮ Spatial decay of discretely self-similar solutions to the Navier-Stokes equations ⋮ Existence of local suitable weak solutions to the Navier-Stokes equations for initial data in \(L^2_{loc} ( \mathbb{R}^3)\) ⋮ Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations ⋮ On the local pressure expansion for the Navier-Stokes equations ⋮ Existence of suitable weak solutions to the Navier-Stokes equations for intermittent data ⋮ Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl ⋮ Characterisation of the pressure term in the incompressible Navier-Stokes equations on the whole space ⋮ Local Energy Solutions to the Navier--Stokes Equations in Wiener Amalgam Spaces

Cites Work

• Unnamed Item
• Forward self-similar solutions of the Navier-Stokes equations in the half space
• Forward discretely self-similar solutions of the Navier-Stokes equations. II
• Discretely self-similar solutions to the Navier-Stokes equations with Besov space data
• On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates
• On Leray's self-similar solutions of the Navier-Stokes equations
• Local energy weak solutions for the Navier-Stokes equations in the half-space
• Existence of discretely self-similar solutions to the Navier-Stokes equations for initial value in \(L_{\mathrm{loc}}^2(\mathbb{R}^3)\)
• Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations
• Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
• Forward discretely self-similar solutions of the Navier-Stokes equations
• The Navier-Stokes Problem in the 21st Century
• Rotationally corrected scaling invariant solutions to the Navier–Stokes equations
• Navier-stokes flow in r³with measures as initial vorticity and morrey spaces
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Self-similar solutions for navier-stokes equations in
• Strong solutions of the Navier-Stokes equation in Morrey spaces
• Well-posedness for the Navier-Stokes equations

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