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We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…

Fluid Dynamics · Physics 2018-08-01 Alexander G. Abanov , Tankut Can , Sriram Ganeshan

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

Analysis of PDEs · Mathematics 2021-10-12 Susanna V. Haziot , Miles. H. Wheeler

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in…

General Relativity and Quantum Cosmology · Physics 2018-03-23 Donato Bini , Carmen Chicone , Bahram Mashhoon

The present study investigates the linear stability of Riemann ellipsoids in both the inviscid limit and in the presence of weak viscosity. In the inviscid regime, we derive a generalised Poincare equation governing small fluid oscillations…

Fluid Dynamics · Physics 2026-02-09 Joris Labarbe

In a recent work [1] the authors studied the dynamics of the interface separating a vacuum from an inviscid incompressible fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid is…

Analysis of PDEs · Mathematics 2015-11-25 Lydia Bieri , Shuang Miao , Sohrab Shahshahani , Sijue Wu

Plane inertial waves are generated using a wavemaker, made of oscillating stacked plates, in a rotating water tank. Using particle image velocimetry, we observe that, after a transient, the primary plane wave is subject to a subharmonic…

Fluid Dynamics · Physics 2012-05-22 Guilhem Bordes , Frédéric Moisy , Thierry Dauxois , Pierre-Philippe Cortet

The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…

Mathematical Physics · Physics 2018-12-04 Nikolay Kuznetsov

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

Mathematical Physics · Physics 2019-01-03 Joachim Escher , David Henry , Boris Kolev , Tony Lyons

A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko's equation considered in \cite{KD}. Both operators in the proposed equation are nonlinear and depend on the…

Mathematical Physics · Physics 2019-06-18 Evgueni Dinvay , Nikolay Kuznetsov

Gaining a fundamental understanding of turbulent flows of dilute polymer solutions has been a challenging and outstanding problem for a long time. In this letter, we examine homogeneous, isotropic polymeric turbulence at large Reynolds and…

Fluid Dynamics · Physics 2025-07-23 Piyush Garg , Marco Edoardo Rosti

This article is concerned with an oceanographic model describing the asymptotic behaviour of a rapidly rotating and incompressible fluid with an inhomogeneous rotation vector; the motion takes place in a thin layer. We first exhibit a…

Analysis of PDEs · Mathematics 2012-07-03 Anne-Laure Dalibard , Laure Saint-Raymond

Wave turbulence describes the long-time statistical behavior of out-of-equilibrium systems composed of weakly interacting waves. Non-Hermitian media ranging from open quantum systems to active materials can sustain wave propagation in…

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…

Analysis of PDEs · Mathematics 2010-02-02 Thomas Alazard , Nicolas Burq , Claude Zuily

This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high-dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the…

Analysis of PDEs · Mathematics 2024-04-08 Amin Esfahani

We consider quasilinear generalizations of the Korteweg-de Vries equation and dispersive perturbations of the Euler equations for compressible fluids, either in Lagrangian or in Eulerian coordinates. In particular, our framework includes…

Analysis of PDEs · Mathematics 2026-02-20 Thomas Courant

In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…

Exactly Solvable and Integrable Systems · Physics 2024-10-14 Rossen I. Ivanov

We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative…

Chaotic Dynamics · Physics 2026-03-30 Ashleigh Simonis , Sergey Nazarenko , Jalal Shatah , Yulin Pan

In this paper, we determine the transversal instability of periodic traveling wave solutions of the generalized Zakharov-Kuznetsov equation in two space dimensions. Using an adaptation of the arguments in \cite{nikolay} in the periodic…

Analysis of PDEs · Mathematics 2023-09-15 Fabio Natali

This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…

Analysis of PDEs · Mathematics 2025-09-22 Liang Li , Quan Wang

The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general…

General Relativity and Quantum Cosmology · Physics 2026-04-01 Benoît Gay , Eugeny Babichev , Sébastien Galtier , Karim Noui