32 citations · 93 across the 12 of their papers we have counts for
13 papers
The -based strong Onsager theorem
Vikram Giri, Hyunju Kwon, Matthew Novack
In this work, we prove the -based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate…
A wavelet-inspired -based convex integration framework for the Euler equations
Vikram Giri, Hyunju Kwon, Matthew Novack
In this work, we develop a wavelet-inspired, -based convex integration framework for constructing weak solutions to the three-dimensional incompressible Euler equations. The m…
An Intermittent Onsager Theorem
Matthew Novack, Vlad Vicol
For any regularity exponent , we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class …
Non-conservative solutions of the Euler- equations
Rajendra Beekie, Matthew Novack
The Euler- equations model the averaged motion of an ideal incompressible fluid when filtering over spatial scales smaller than . We show that there exists such that we…
Exact Boundary Controllability for the Ideal Magneto-hydrodynamic Equations
Igor Kukavica, Matthew Novack, Vlad Vicol
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition…
Enhanced dissipation and Hörmander's hypoellipticity
Dallas Albritton, Rajendra Beekie, Matthew Novack
We examine the phenomenon of enhanced dissipation from the perspective of Hörmander's classical theory of second order hypoelliptic operators [31]. Consider a passive scalar in a s…
Non-conservative weak solutions of the incompressible 3D Euler equations
Tristan Buckmaster, Nader Masmoudi, Matthew Novack +1
For any positive regularity parameter , we construct non-conservative weak solutions of the 3D incompressible Euler equations which lie in uniformly in time. In…
Classical Solutions for the 3D Quasi-Geostrophic System on a Bounded Domain
Matthew Novack, Alexis Vasseur
We revisit a model for three-dimensional, inviscid quasi-geostrophic flow on bounded, cylindrical domains introduced by the authors in \cite{nv18}. We prove the local-in-time exist…
Variational methods for the kinetic Fokker-Planck equation
D. Albritton, S. Armstrong, J. -C. Mourrat +1
We develop a functional analytic approach to the study of the Kramers and kinetic Fokker-Planck equations which parallels the classical theory of uniformly elliptic equations…
Non-uniqueness of Weak Solutions to the 3D Quasi-Geostrophic Equations
Matthew Novack
We show that weak solutions to the 3D quasi-geostrophic system in the class for are not unique and may achieve any smooth, non-negative energy profile.…
The Inviscid 3D Quasi-Geostrophic System on Bounded Domains
Matthew Novack, Alexis Vasseur
We present a formal derivation of the inviscid 3D quasi-geostrophic system (QG) from primitive equations on a bounded, cylindrical domain. A key point in the derivation is the trea…
On the Weak Solutions to the 3D Inviscid Quasi-Geostrophic System
Matthew D. Novack
The purpose of this note is to study the weak solutions to the inviscid quasi-geostrophic system for initial data belonging to Lebesgue spaces. We give a global existence result as…
Global in Time Classical Solutions to the 3D Quasi-geostrophic System for Large Initial Data
Matthew D. Novack, Alexis F. Vasseur
In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly lar…