相关论文: Downscaling data assimilation algorithm with appli…

Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from…

Time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system is studied. Concerning the linearized problem, the decay estimate with diffusion wave property for an initial data is derived. As an application, the time…

This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…

The renormalization group approach and the operator product expansion technique are applied to the model of a tracer field advected by the Navier-Stokes velocity ensemble for a compressible fluid. The model is considered in the vicinity of…

We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…

The goal of this paper is to provide an algorithm that, for any sufficiently localised, divergence-free small initial data, explicitly constructs a localised external force leading to a rapidly dissipative solutions of the Navier-Stokes…

We construct solutions to the Navier-Stokes equations on $\mathbf{R}^2$ with an arbitrary number of stagnation points which merge and split along trajectories that can be prescribed freely, up to a small deformation.

Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the…

We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are probability measures accounting for spatial correlations, and…

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

In this paper statistical solutions of the 3D Navier-Stokes-$\alpha$ model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-$\alpha$ model…

This work introduces a variant of resolvent analysis that identifies forcing and response modes that are sparse in both space and time. This is achieved through the use of a sparse principal component analysis (PCA) algorithm, which…

We construct a solution to the spatially periodic $d$-dimensional Navier-Stokes equations with a given distribution of the initial data. The solution takes values in the Sobolev space $H^\alpha$, where the index $\alpha\in R$ is fixed…

In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this…

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

We consider solutions to the 2d Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}$ close to the Poiseuille flow, with small viscosity $\nu>0$. Our first result concerns a semigroup estimate for the linearized problem. Here we show that…

In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of interest is a recursive feedback control-based algorithm that…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…