English
Related papers

Related papers: Well-posedness and long-term behaviour for a tropo…

200 papers

We establish the global well-posedness of classical solutions to the vacuum free boundary problem of the 1-D viscous Saint-Venant system with large data. Since the depth $\rho$ of the fluid vanishes on the moving boundary, the momentum…

Analysis of PDEs · Mathematics 2025-04-15 Xin Zhouping , Zhang Jiawen , Zhu Shengguo

Should it be a pebble hitting water surface or an explosion taking place underwater, concentric surface waves inevitably propagate. Except for possibly early times of the impact, finite amplitude concentric water waves emerge from a balance…

Fluid Dynamics · Physics 2024-05-28 R. Krechetnikov

We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…

Analysis of PDEs · Mathematics 2023-10-02 E. Abdo , M. Ignatova

A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…

Fluid Dynamics · Physics 2023-07-26 R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni , T. T. Vu Ho

Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and…

Analysis of PDEs · Mathematics 2014-03-07 Aimin Huang

Sunspots are transient, magnetically intense features that host oscillations linked to magnetohydrodynamic (MHD) waves. These waves may contribute to plasma heating and drive mass flows in the solar wind. Beyond their energetic role, they…

Solar and Stellar Astrophysics · Physics 2026-05-20 Kartika Sangal , A. K. Srivastava , Libo Fu , Ding Yuan , Song Feng , Yuandeng Shen

We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…

Soft Condensed Matter · Physics 2013-03-12 Michel Destrade , Giuseppe Saccomandi

The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…

Classical Physics · Physics 2025-03-20 Mariano Caruso , Guillermo Rus , Juan Melchor

The intermediate nonlinear Schr\"odinger equation (INLS) describes the dynamics of the envelope of weakly nonlinear internal waves in a stratified fluid of finite depth. While the INLS equation is known to admit dark soliton solutions,…

Analysis of PDEs · Mathematics 2026-05-26 Takafumi Akahori , Rana Badreddine , Slim Ibrahim , Nobu Kishimoto

When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…

We consider an incompressible viscous flow without surface tension in a finite- depth domain of three dimension, with free top boundary. This system is governed by a Naiver-Stokes equation in a moving domain and a transport equation for the…

Analysis of PDEs · Mathematics 2014-12-09 Lei Wu

We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…

Analysis of PDEs · Mathematics 2018-10-09 Andrii Anikushyn , Michael Pokojovy

We consider the one-dimensional shallow water problem with capillary surfaces and moving contact {lines}. An energy-based model is derived from the two-dimensional water wave equations, where we explicitly discuss the case of a stationary…

Analysis of PDEs · Mathematics 2024-01-10 Jiaxu Li , Xin Liu , Dirk Peschka

We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…

Pattern Formation and Solitons · Physics 2009-11-10 Patrick N. McGraw , Michael Menzinger

We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…

Analysis of PDEs · Mathematics 2022-06-16 Apratim Bhattacharya , Markus Gahn , Maria Neuss-Radu

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…

Analysis of PDEs · Mathematics 2026-05-08 Chenyun Luo , Junyan Zhang

Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…

Chaotic Dynamics · Physics 2007-05-23 Takeshi Ogasawara , Sadayoshi Toh

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p $\in$ [2, $\infty$]. Some…

Analysis of PDEs · Mathematics 2019-07-30 Yacine Chitour , Swann Marx , Christophe Prieur

We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…

Mathematical Physics · Physics 2020-03-12 Stéphane Dartois , Oleg Evnin , Luca Lionni , Vincent Rivasseau , Guillaume Valette

Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…

Pattern Formation and Solitons · Physics 2026-04-14 David Pinto-Ramos