Related papers: Detectability and global observer design for 2D Na…
The paper deals with the stochastic two-dimensional Navier-Stokes equation for incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form $G\, dW$, where $W$ is a cylindrical…
We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme utilizing new stationary building blocks designed…
This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case…
Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy…
We study constant input delay compensation by using finite-dimensional observer-based controllers in the case of the 1D heat equation. We consider Neumann actuation with nonlocal measurement and employ modal decomposition with $N+1$ modes…
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the…
This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…
Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density…
A general class of linear advective PDEs, whose leading order term is of viscous dissipative type, is considered. It is proved that beyond the limit of the essential spectrum of the underlying inviscid operator, the eigenvalues of the…
Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $\epsilon$. So far, there is no effective \'a…
Let G be the (open) set of~$\dot H^{\frac 1 2}$ divergence free vector fields generating a global smooth solution to the three dimensional incompressible Navier-Stokes equations. We prove that any element of G can be perturbed by an…
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…
This work addresses the design of a robust hybrid observer for discrete-time switched linear systems subject to unknown inputs and modeling errors. The observer herein proposed is synthesized, for the case when the active mode is unknown…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
A local anisotropic geometric measure-type condition on the super-level sets of solutions to the 3D NSE preventing the formation of finite-time singularity is presented; essentially, local one-dimensional sparseness of the regions of…
Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…
This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order $N \geq 1$. The convergence of the…
We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of…
This paper addresses the emulation-based observer design for networked control systems (NCS) with linear plants that operate at two time scales in the presence of measurement noise. The system is formulated as a hybrid singularly perturbed…
We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…