Long-time asymptotics for the damped Boussinesq equation in a disk.
Long-time asymptotics of solutions for the second initial-boundary value problem for the damped Boussinesq equation.
Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations
In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...
Mathematical study of rotational incompressible non-viscous flows through multiply connected domains
The paper is devoted to the study of the boundary value problem for an elliptic quasilinear second-order partial differential equation in a multiply connected, bounded plane domain under the assumption that the Dirichlet boundary value conditions on the separate components of the boundary are given up to additive constants. These constants together with the solution of the equation considered are to be determined so as to fulfil the so called trainling conditions. The results have immediate applications...
Mechanical analogy for the wave-particle: Helix on a vortex filament.
Mixed Finite Element Approximation of the Vector Potential.
Modeling of coupled roll and yaw damping of a floating body in waves.
Modelling geophysical flows in the equatorial zone
We present here a series of works which aims at describing geophysical flows in the equatorial zone, taking into account the dominating influence of the earth rotation. We actually proceed by successive approximations computing for each model the response of the fluid to the strong Coriolis penalisation. The main difficulty is due to the spatial variations of the Coriolis acceleration : in particular, as it vanishes at the equator, fast oscillations are trapped in a thin strip of latitudes.
Modulational stability of Korteweg-de Vries and Boussinesq wavetrains.
Motion of two point vortices in a steady, linear, and elliptical flow.
Multigrid Methods for Boundary Integral Equations.
Multiple spatial scales in engineering and atmospheric low Mach number flows
The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of this...
Multiple spatial scales in engineering and atmospheric low Mach number flows
The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of...
Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution.
Nested axi-symmetric vortex rings
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
Non existence of standing waves for hyperbolic Davey-Stewartson systems
Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation.
Nonlinear diffraction of water waves by offshore structures.
Nonlinear instability in an ideal fluid