On the global stability of smooth solutions of the Navier-Stokes equations

DOI10.1016/j.aml.2020.106970zbMath1462.35249OpenAlexW3116137244MaRDI QIDQ1996363

Livio Pizzocchero

Publication date: 4 March 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106970

zbMATH Keywords

Navier-Stokes equationsglobal stabilityexistence and regularity theory

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large order Reynolds expansions for the Navier-Stokes equations
• On approximate solutions of the incompressible Euler and Navier-Stokes equations
• Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations
• Smooth solutions of the Euler and Navier-Stokes equations from the a posteriori analysis of approximate solutions
• Vortex reconnection in the three dimensional Navier-Stokes equations
• An \(H^1\) setting for the Navier-Stokes equations: quantitative estimates
• On the constants in a basic inequality for the Euler and Navier-Stokes equations
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Global stability of large solutions to the 3D Navier-Stokes equations
• Bilinear estimates in \(BMO\) and the Navier-Stokes equations
• New results on the constants in some inequalities for the Navier-Stokes quadratic nonlinearity
• On the constants in a Kato inequality for the Euler and Navier-Stokes equations
• Beltrami fields with hyperbolic periodic orbits enclosed by knotted invariant tori
• On approximate solutions of the equations of incompressible magnetohydrodynamics
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• On the Reynolds number expansion for the Navier-Stokes equations
• Lower bounds on blow up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces
• A posteriori regularity of the three-dimensional Navier–Stokes equations from numerical computations
• ON APPROXIMATE SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS II: GENERALIZATIONS, AND APPLICATIONS TO NAVIER–STOKES EQUATIONS
• Exact Solutions of the Unsteady Navier-Stokes Equations
• Exact fully 3D Navier–Stokes solutions for benchmarking
• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations

This page was built for publication: On the global stability of smooth solutions of the Navier-Stokes equations