On the Existence of Helical Invariant Solutions to Steady Navier--Stokes Equations

DOI10.1137/20M1343324zbMath1497.35375arXiv2102.13341OpenAlexW3134921805MaRDI QIDQ5092883

Shangkun Weng, Wenqi Lyu, Mikhail V. Korobkov

Publication date: 26 July 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.13341

zbMATH Keywords

steady Navier-Stokes equationshelically symmetric flow

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Symmetries, invariants, etc. in context of PDEs (35B06)

Cites Work

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• Planar limits of three-dimensional incompressible flows with helical symmetry
• Global existence of weak solutions to the three-dimensional Euler equations with helical symmetry
• Liouville theorems for the Navier-Stokes equations and applications
• The existence theorem for the steady Navier-Stokes problem in exterior axially symmetric 3D domains
• Helically symmetric solutions to the 3D Navier-Stokes equations for compressible isentropic fluids
• Invariant helical subspaces for the Navier-Stokes equations
• Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data
• On spaces of solenoidal vector fields and boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries
• Note on the flux problem for stationary incompressible Navier-Stokes equations in domains with a multiply connected boundary
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• On the existence of a stationary symmetric solution of the two- dimensional fluid flow problem
• Compensated compactness and Hardy spaces
• On the Morse-Sard property and level sets of Sobolev and BV functions
• On the flux problem in the theory of steady Navier-Stokes equations with nonhomogeneous boundary conditions
• Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains
• On the Morse-Sard property and level sets of \(W^{n,1}\) Sobolev functions on \(\mathbb{R}^n\)
• A note on the exterior two-dimensional steady-state Navier-Stokes problem
• On the steady-state solutions of the Navier-Stokes equations. III
• Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry
• A remark on the existence of 2-D steady Navier-Stokes flow in bounded symmetric domain under general outflow condition
• On the existence of solutions to the stationary Navier-Stokes equations
• Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking
• The existence theorem for steady Navier-Stokes equations in the axially symmetric case
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Lower Bound on the Blow-up Rate of the Axisymmetric Navier–Stokes Equations
• The co-area formula for Sobolev mappings
• Global Existence and Uniqueness of Weak Solutions of Three-Dimensional Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching
• Lectures on Navier-Stokes Equations

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