70 citations · 323 across the 27 of their papers we have counts for
22 papers · 1 filter
Nonlocal Boundary Conditions for Truncated-Fractional Differential Equations Posed on Bounded Domains
Mikil Foss, Adam Larios, Michael Pieper
Nonlocal models have found great success in recent years. In particular, models that replace spatial derivatives with strongly singular integral operators involving finite interact…
Application of Continuous Data Assimilation in High-Resolution Ocean Modeling
Adam Larios, Mark R. Petersen, Collin Victor
We demonstrate a formulation of the Azouani-Olson-Titi (AOT) algorithm in the MPAS-Ocean implementation of the primitive equations of the ocean, presenting global ocean simulations…
Continuous Data Assimilation for the 3D and Higher-Dimensional Navier--Stokes equations with Higher-Order Fractional Diffusion
Adam Larios, Collin Victor
We study the use of the Azouani-Olson-Titi (AOT) continuous data assimilation algorithm to recover solutions of the Navier--Stokes equations modified to have higher-order fractiona…
Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm
Elizabeth Carlson, Adam Larios, Edriss S. Titi
We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give…
The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier-Stokes equations
Adam Larios, Yuan Pei, Collin Victor
We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "d…
Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three
Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability crite…
The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations
Trenton Franz, Adam Larios, Collin Victor
We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations.…
Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
Adam Larios, Elizabeth Carlson
We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations. Moreo…
On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
Adam Larios, Kazuo Yamazaki
The Kuramoto-Sivashinsky equations (KSE) arise in many diverse scientific areas, and are of much mathematical interest due in part to their chaotic behavior, and their similarity t…
Parameter Recovery and Sensitivity Analysis for the 2D Navier-Stokes Equations Via Continuous Data Assimilation
Elizabeth Carlson, Joshua Hudson, Adam Larios
We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown Reynolds number. We determine the large-time error between…
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
Adam Larios, Collin Victor
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as tim…
Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data
Adam Larios, Yuan Pei
We propose a data assimilation algorithm for the 2D Navier-Stokes equations, based on the Azouani, Olson, and Titi (AOT) algorithm, but applied to the 2D Navier-Stokes-Voigt equati…
Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations
Adam Larios, Yuan Pei, Leo Rebholz
The velocity-vorticity formulation of the 3D Navier-Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose…
Continuous data assimilation for the magnetohydrodynamic equations in 2D using one component of the velocity and magnetic fields
Animikh Biswas, Joshua Hudson, Adam Larios +1
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently lar…
Nonlinear Continuous Data Assimilation
Adam Larios, Yuan Pei
We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Ol…
On the local well-posedness and a Prodi-Serrin type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
Adam Larios, Yuan Pei
We prove a Prodi-Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of…
A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization
Adam Larios, Mark Petersen, Edriss S. Titi +1
We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related…
A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization
Adam Larios, Edriss S. Titi
We propose a new blow-up criterion for the 3D Euler equations of incompressible fluid flows, based on the 3D Euler-Voigt inviscid regularization. This criterion is similar in chara…
Global Regularity vs. Finite-Time Singularities: Some Paradigms on the Effect of Boundary Conditions and Certain Perturbations
Adam Larios, Edriss S. Titi
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems involving nonlinear partial differential equations, we provide several cautionary…
Higher-Order Global Regularity of an Inviscid Voigt-Regularization of the Three-Dimensional Inviscid Resistive Magnetohydrodynamic Equations
Adam Larios, Edriss S. Titi
We prove existence, uniqueness, and higher-order global regularity of strong solutions to a particular Voigt-regularization of the three-dimensional inviscid resistive Magnetohydro…
Global Well-posedness for The 2D Boussinesq System Without Heat Diffusion and With Either Anisotropic Viscosity or Inviscid Voigt- Regularization
Adam Larios, Evelyn Lunasin, Edriss S. Titi
We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean…
On the Higher-Order Global Regularity of the Inviscid Voigt-Regularization of Three-Dimensional Hydrodynamic Models
Adam Larios, Edriss S. Titi
We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid -regularization of the three-dimensional Euler equations of ideal…