Related papers: Continuous data assimilation for the 3D primitive …
Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…
AI emulators for forecasting have emerged as powerful tools that can outperform conventional numerical predictions. The next frontier is to build emulators for long climate simulations with skill across a range of spatiotemporal scales, a…
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…
We prove the existence and uniqueness of global, classical solutions to the 3D Muskat problem in the stable regime whenever the initial interface has sublinear growth and slope $||\nabla_x f_0||_{L^\infty}< 5^{-1/2}$. We show under these…
In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We consider fully discrete numerical schemes for a downscaling data assimilation algorithm aimed at approximating the velocity field of the 2D Navier-Stokes equations corresponding to given coarse mesh observational measurements. The time…
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…
A real time assimilation and forecasting system for coastal currents is presented. The purpose of the system is to deliver current analyses and forecasts based on assimilation of high frequency radar surface current measurements. The local…
We establish long-time existence of smooth solutions to the 2D ideal Boussinesq equations and to the 2D non-homogeneous incompressible Euler equations for initial data consisting of small temperature perturbations, or small density…
For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.
We study bounded ancient solutions of the Navier-Stokes equations. These are the solutions which are defined for all past time. In two space dimensions we prove that such solutions are either constant or functions of time only, depending on…
This article examines the accuracy for large times of asymptotic expansions from periodic homogenization of wave equations. As usual, $\epsilon$ denotes the small period of the coefficients in the wave equation. We first prove that the…
We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported initial data with sufficiently small…
Forecasting ocean drift trajectories are important for many applications, including search and rescue operations, oil spill cleanup and iceberg risk mitigation. In an operational setting, forecasts of drift trajectories are produced based…
In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
In this paper we consider the equation for equivariant wave maps from $R^{3+1}$ to $S^3$ and we prove global in forward time existence of certain $C^\infty$-smooth solutions which have infinite critical Sobolev norm…
This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies developing novel schemes with an understanding of the rich…
With the success of machine learning (ML) applied to climate reaching further every day, emulators have begun to show promise not only for weather but for multi-year time scales in the atmosphere. Similar work for the ocean remains nascent,…