Related papers: Steady state existence of passive vector fields un…
In this paper, we solve a long-standing open problem: nonlinear stability of current-vortex sheet in the ideal incompressible Magneto-Hydrodynamics under the linear stability condition. This result gives a first rigorous confirmation of the…
We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and…
We study the Navier-Stokes steady states for a low density monodisperse hard sphere granular gas (i.e, a hard sphere ideal monatomic gas with inelastic interparticle collisions). We present a classification of the uniform steady states that…
In this paper, we exhibit non-uniqueness of Leray weak solutions of the forced magnetohydrodynamic (MHD for short) equations. Similar to the solutions constructed in \cite{ABC2}, we first find a special steady solution of ideal MHD…
We establish a variational framework for nonlinear instabilities in a setting of the ideal magnetohydrodynamic (MHD) equations. We apply a variational method to various kind of smooth steady states which are shown to be nonlinearly unstable…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the ground states coincide with the…
We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an…
Physical experiments and numerical simulations have observed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and damps electrically conducting fluids. This paper intends to establish this phenomenon as a…
The idea of using Feed-Forward Neural Networks (FFNNs) as regression functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to models herein named Neural NARXs (NNARXs), has been quite popular in the early days of machine…
In this article we study the one-dimensional, asymptotically linear, non-linear Schr\"odinger equation (NLS). We show the existence of a global smooth curve of standing waves for this problem, and we prove that these standing waves are…
We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present also numerical experiments indicating uniqueness and…
We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinear stability of steady states which are decreasing functions…
This article studies a class of semilinear scalar field equations on the real line with variable coefficients in the linear terms. These coefficients are not necessarily small perturbations of a constant. We prove that under suitable…
We study material lines and passive vectors in a model of turbulent flow at infinite-Reynolds number, the Kraichnan-Kazantsev ensemble of velocities that are white-noise in time and rough (Hoelder continuous) in space. It is argued that the…
We consider stochastic mSQG (modified Surface Quasi-Geostrophic) equations with multiplicative transport noise of Kraichnan type, and $L^p$-initial conditions. Inspired by the recent work of Coghi and Maurelli [arXiv:2308.03216], we show…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the…