We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators,
that are general, robust, and versatile. We use these nonlinear bounds to provide …

This paper establishes the global in time existence of classical solutions to the two-
dimensional anisotropic Boussinesq equations with vertical dissipation. When only vertical …

An algorithm for continuous data assimilation for the two-dimensional Bénard convection
problem is introduced and analyzed. It is inspired by the data assimilation algorithm …

We establish global existence and uniqueness theorems for the two-dimensional non-
diffusive Boussinesq system with anisotropic viscosity acting only in the horizontal direction …

The two-dimensional incompressible Boussinesq equations with partial or fractional
dissipation have recently attracted considerable attention and the global regularity issue has …

Understanding the impact of model error on data assimilation is an important practical topic.
Model error in the subgrid scale is commonly seen in various applications as a natural …

This paper investigates the global (in time) regularity of solutions to a system of equations
that generalize the vorticity formulation of the 2D Boussinesq–Navier–Stokes equations. The …

Data assimilation is a methodology to estimate weather or ocean variables by combining
(synchronizing) information from observational data with a numerical dynamical (forecast) …

Global Smooth Solutions to the n-Dimensional Damped Models of Incompressible Fluid
Mechanics with Small Initial Datum | SpringerLink Skip to main content Advertisement …

Abstract The two-dimensional (2D) incompressible Euler equations have been thoroughly
investigated and the resolution of the global (in time) existence and uniqueness issue is …