相关论文: Parameter analysis in continuous data assimilation…
In this work, we study the Cauchy problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation with rapid attenuation of initial data. The basis Riemann-Hilbert problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…
This paper studies a coupled two-dimensional Navier--Stokes--Cahn--Hilliard phase-field model augmented by a transported auxiliary field, and develops a continuous data assimilation (CDA) framework for recovering its trajectories from…
By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of…
In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant multiple of the density's power ($\rho^\delta$ with…
Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which…
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the…
The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly…
This paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the Navier-Stokes-Cahn-Hilliard system in one dimensional space.…
In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
In this work, we investigate the existence and uniqueness of solutions to the following 2D and 3D convective Brinkman-Forchheimer extended Darcy equations defined on a bounded smooth domain $\Omega\subset\mathbb{R}^d$, $d\in\{2,3\}$,…
This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context of the two-dimensional (2D) Navier-Stokes…
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann-Hilbert…
In this study, we conduct a parameter error analysis for the 3D modified Leray-$\alpha$ model using both analytical and numerical approaches. We first prove the global well-posedness and continuous dependence of initial data for the…
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
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…