Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations
DOI10.1002/cpa.22084arXiv1912.10091MaRDI QIDQ6074557
Publication date: 12 October 2023
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.10091
incompressible Navier-Stokes equationssurface tensionfree boundarymoving upper boundariesoverdetermined Stokes problemtraveling velocity
Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Boundary value problems for PDEs with pseudodifferential operators (35S15) Capillarity (surface tension) for incompressible viscous fluids (76D45) Free boundary problems for PDEs (35R35) Traveling wave solutions (35C07) Moving boundary problems for PDEs (35R37) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)
Related Items
Cites Work
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
- Two dimensional water waves in holomorphic coordinates II: global solutions
- Cauchy theory for the gravity water waves system with non-localized initial data
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- ``Graph paper trace characterizations of functions of finite energy
- The compressible viscous surface-internal wave problem: stability and vanishing surface tension limit
- On the wind generation of water waves
- Local well-posedness of the viscous surface wave problem without surface tension
- Global solutions for 2D quadratic Schrödinger equations
- On the Cauchy problem for gravity water waves
- Solitary water waves of large amplitude generated by surface pressure
- Two dimensional water waves in holomorphic coordinates
- Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations
- Global wellposedness of the 3-D full water wave problem
- On the water-wave equations with surface tension
- Solvability of the free boundary value problem of the Navier-Stokes equations
- Free boundary value problems for the stationary Navier-Stokes equations in domains with noncompact boundaries
- Large-time regularity of viscous surface waves
- Exact solitary water waves with vorticity
- Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
- Decaying solution of a Navier-Stokes flow without surface tension
- Resolvent estimates for the Stokes operator on an infinite layer.
- New estimates for elliptic equations and Hodge type systems
- Steady periodic capillary waves with vorticity
- Almost global wellposedness of the 2-D full water wave problem
- Free surface of the steady flow of a Newtonian fluid in a finite channel
- On solitary water-waves of finite amplitude
- On the Stokes conjecture for the wave of extreme form
- Manifolds, tensor analysis, and applications.
- On the solvability of the Stokes and Navier-Stokes problems in the domains that are layer-like at infinity
- The asymptotic properties of the solution to the Stokes problem in domains that are layer-like at infinity
- Travelling wave-like solutions of the Navier-Stokes and the related equations
- Well-posedness in Sobolev spaces of the full water wave problem in 2D
- Stokes waves
- On a resolvent estimate of the Stokes equation on an infinite layer.
- On a resolvent estimate of the Stokes equation on an infinite layer. II: \( \lambda=0\) case
- Free surface problem of stationary non-Newtonian fluids
- Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension
- Travelling waves in dilatant non-Newtonian thin films
- Existence and qualitative theory for stratified solitary water waves
- Global solution for the 3D gravity water waves system above a flat bottom
- A variational reduction and the existence of a fully localised solitary wave for the three-dimensional water-wave problem with weak surface tension
- Global solutions of the gravity-capillary water-wave system in three dimensions
- Traveling waves bifurcating from plane Poiseuille flow of the compressible Navier-Stokes equation
- Reduced and generalized Stokes resolvent equations in asymptotically flat layers. I: Unique solvability
- Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus
- Convexity of Stokes waves of extreme form
- Large-time existence of surface waves in incompressible viscous fluids with or without surface tension
- Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
- Almost exponential decay of periodic viscous surface waves without surface tension
- On a stationary problem of the Stokes equation in an infinite layer in Sobolev and Besov spaces
- Zero surface tension limit of viscous surface waves
- Global solutions for the gravity water waves system in 2d
- On the existence of non-flat profiles for a Bernoulli free boundary problem
- Decay of solutions to the linearized free surface Navier-Stokes equations with fractional boundary operators
- Traces for homogeneous Sobolev spaces in infinite strip-like domains
- Existence, nonexistence, and asymptotics of deep water solitary waves with localized vorticity
- Phase transitions and traveling waves in compressible fluids
- Steady stratified periodic gravity waves with surface tension. I: Local bifurcation.
- Steady stratified periodic gravity waves with surface tension. II: Global bifurcation.
- Decay of viscous surface waves without surface tension in horizontally infinite domains
- Fully localised solitary-wave solutions of the three-dimensional gravity -- capillary water-wave problem
- The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces
- Global in time behavior of viscous surface waves: horizontally periodic motion
- On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions
- Global solutions and asymptotic behavior for two dimensional gravity water waves
- Steady Water Waves in the Presence of Wind
- Large-Amplitude Solitary Water Waves with Vorticity
- Well-Posedness and Decay of the Viscous Surface Wave
- Report on a local in time solvability of free surface problems for the Navier–Stokes equations with surface tension
- Resonantly forced gravity–capillary lumps on deep water. Part 1. Experiments
- Resonantly forced gravity–capillary lumps on deep water. Part 2. Theoretical model
- Steady water waves
- Steady Periodic Capillary‐Gravity Waves with Vorticity
- Sobolev estimates for two dimensional gravity water waves
- On the free boundary problem of three-dimensional incompressible Euler equations
- Stratified Steady Periodic Water Waves
- Small divisor problem in the theory of three-dimensional water gravity waves
- The initial value problem for the navier-stokes equations with a free surface
- The existence of solitary water waves
- On the existence of a wave of greatest height and Stokes’s conjecture
- On the existence theory for irrotational water waves
- Well-posedness in Sobolev spaces of the full water wave problem in 3-D
- The Stokes and Krasovskii Conjectures for the Wave of Greatest Height
- Exact steady periodic water waves with vorticity
- A First Course in Sobolev Spaces
- Global Regularity for 2d Water Waves with Surface Tension
- Steady Water Waves
- Asymptotics of solutions of the stationary Navier-Stokes system of equations in a domain of layer type
- Well-posedness of the water-waves equations
- A Proof of the Stokes Conjecture in the Theory of Surface Waves*
- Free boundary problems for nonstationary Navier–Stokes equations
- On the regularity of the composition of diffeomorphisms
- Global Existence for Capillary Water Waves
- The Viscous Surface Wave Problem with Generalized Surface Energies
- Experimental observation of gravity–capillary solitary waves generated by a moving air suction
- Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions
- On the theory of steady-state waves of finite amplitude