Related papers: Well-posedness of a water wave model with viscous …

In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other…

The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there are instances where the viscous damping…

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are…

This paper is concerned with the Cauchy problem of the one-dimensional free surface equation of shallow water wave, we obtain local well-posedness of the free surface equation of shallow water wave in Sobolev spaces. In addition, we also…

We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation.…

We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…

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…

In this paper, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with free top boundary and fixed bottom boundary. This system is governed by a Naiver-Stokes equation in above…

In this paper we study solitary traveling wave solutions to a damped shallow water system, which is in general quasilinear and of mixed type. We develop a small data well-posedness theory and prove that traveling wave solutions are a…

The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…

We consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free…

Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed ``odd viscosity'', becomes…

We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.

We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The…

We study the theory of relativistic viscous hydrodynamics introduced in arXiv:1109.0985 and arXiv:1907.12695, which provided a causal and stable first-order theory of relativistic fluids with viscosity in the case of barotropic fluids. The…

We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on…

We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…

In this paper, we prove the local well-posedness of the water wave problem with surface tension in the case of finite depth by working in the Eulerian setting. For the flat bottom, as surface tension tends to zero, the solution of the water…