相关论文: Continuous data assimilation for the three dimensi…

We present a target field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetisation is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the…

We consider the phenomenon of magnetic reconnection, namely a change in the topology of magnetic lines, for sufficiently regular solutions of the three-dimensional periodic magnetohydrodynamic (MHD) equations. We provide examples where…

We present a method for implementing the constraints that are implied by Maxwell's equations in fits to measurements of the magnetic field in the muon storage ring of the $g-2$ experiment. The method that we use makes use of…

A previously published analytical magnetohydrodynamic model for the local interstellar magnetic field in the vicinity of the heliopause (R\"oken et al. 2015) is extended from incompressible to compressible, yet predominantly subsonic flow,…

We study the large field limit in Schr\"odinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. In a first step, using regular perturbation theory, we derive an…

Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a…

In this paper, we investigate the two-dimensional incompressible primitive equations with fractional horizontal dissipation. Specifically, we establish global well-posedness of strong solutions for arbitrarily large initial data when the…

In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the…

We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely…

Continuous data assimilation (CDA) techniques, most notably the nudging approach proposed by Azouani, Olson, and Titi (AOT), have been shown to be very successful in deterministic frameworks for achieving long-time synchronization between…

We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove…

We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where $\Phi:\mathcal…

In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…

Magnetic particles underpin a broad range of technologies, from water purification and mineral processing to bioseparations and targeted drug delivery. The dynamics of magnetic particles in high-gradient magnetic fields-encompassing both…

We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill--posed in the class of weak solutions for a large class of physically admissible data.…

This paper is concerned with the asymptotic properties of the small data solutions to the massless Vlasov-Maxwell system in $3d$. We use vector field methods to derive almost optimal decay estimates in null directions for the…

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…

In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…

This paper improves the spectrally-filtered direct-insertion downscaling method for discrete-in-time data assimilation by introducing a relaxation parameter that overcomes a constraint on the observation frequency. Numerical simulations…

This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant…