7 papers
Long-wave instability of periodic shear flows with constant magnetic field for the 2D resistive MHD equations
Roberto Feola, Luca Franzoi, Riccardo Montalto +1
We investigate the long-wave linear stability and instability of the two-dimensional viscous, resistive Magnetohydrodynamic (MHD) equations, in vorticity-current formulation, on th…
Nonlinear Instability in the 2D Kuramoto-Sivashinsky equation
David M. Ambrose, Anna L. Mazzucato, Riccardo Montalto
In this paper we analyze the Kuramoto-Sivashinsky equation (KSE), a model of flame-front propagation, on a two-dimensional square torus of arbitrary size with . In thi…
The Vanishing Viscosity Limit and Boundary Layers for Symmetric Fluid Flows with Anisotropic Viscosity
Valentina Galbiati, Anna Mazzucato, Riccardo Montalto
We study the vanishing viscosity limit for the incompressible Navier-Stokes equations with anisotropic viscosity in bounded domains, analyzing certain classes of symmetric flows: p…
Quasi-resonant normal form and quadratic lifespan for 3D gravity-capillary water waves
Roberto Feola, Riccardo Montalto, Federico Murgante
We study the long-time dynamics of small-amplitude solutions to the three-dimensional gravity-capillary water waves equations for an inviscid and irrotational fluid with periodic b…
Long time dynamics close to large amplitude quasi-periodic traveling waves in two dimensional forced rotating fluids
Roberto Feola, Luca Franzoi, Riccardo Montalto
In this paper we consider the -plane equation with a smooth external force which is a quasi-periodic traveling wave of large amplitude , , and with large…
Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations
Maria Colombo, Michele Dolce, Riccardo Montalto +1
In 1959, Kolmogorov proposed to study the instability of the shear flow in the vanishing viscosity regime in tori . This question was l…