Matthew Novack

About Me

I am an associate professor in the Department of Mathematics at the University of Notre Dame.  My research interests lie in partial differential equations, particularly those arising in fluid dynamics, kinetic theory, and related fields. 

My CV can be found here.

My research is partially supported by the National Science Foundation, Division of Mathematical Sciences, through NSF Grant DMS-2307357 .

Publications

17.  V. Giri, H. Kwon, and M. Novack - Non-conservation of a generalized helicity in the Euler equations.  arXiv .  

16.  E. Ashkarian, A. Bhargava, N. Gismondi, M. Novack - Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces.  arXiv .

15.  D. Albritton, J. Bedrossian, M. Novack - Kinetic shock profiles for the Landau equation. arXiv .  Ars Inveniendi Analytica, Paper No. 1, 2026 .  

14.  V. Giri, H. Kwon, and M. Novack - The L3-based strong Onsager theorem.  arXiv . Annals of Mathematics, Volume 204, Issue 1, 2026 .

13.  M. Novack - Scaling laws and exact results in turbulence.  arXiv .  Nonlinearity, Volume 37, Number 9, 2024.

12.  V. Giri, H. Kwon, and M. Novack - A wavelet-inspired, L3-based convex integration framework for the Euler equations.  arXiv .  Annals of PDE, Volume 10, Article 19, 2024.   Errata .

11.  M. Novack and V. Vicol - An Intermittent Onsager Theorem - arXiv . Inventiones mathematicae, Volume 233, 2023 .

10.  R. Beekie and M. Novack - Non-conservative Solutions to the Euler-alpha Equations - arXiv . Journal of Mathematical Fluid Mechanics, Volume 25, Article number 22 (2023) .

9.  D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack - Variational Methods for the Kinetic Fokker-Planck Equation - arXiv .  Analysis & PDE, Volume 17, Number 6, 2024 .

8.  I. Kukavica, M. Novack, and V. Vicol - Exact Boundary Controllability for the Ideal Magneto-hydrodynamic Equations - arXiv .  Journal of Differential Equations 318 (2022), 94-112 .

7.  D. Albritton, R. Beekie, and M. Novack - Enhanced Dissipation and Hörmander's Hypoellipticity - arXiv. Journal of Functional Analysis, Volume 283, Issue 3, August 2022 .

6.  T. Buckmaster, N. Masmoudi, M. Novack, and V. Vicol - Non-conservative H1/2- weak solutions of the incompressible 3D Euler equations - arXiv. Annals of Mathematics Studies, AMS 217 .

5.  M. Novack and A. Vasseur - Classical Solutions for the 3D Quasi-Geostrophic System on a Bounded Domain - arXiv.   Physica D, Volume 404 (2020), no. 132362, 8 pp .

4.  M. Novack - Non-uniqueness of Weak Solutions to the 3D Quasi-Geostrophic Equations - arXiv.  SIAM J. Math. Analysis, Volume 52 (2020), no. 4, 3301-3349 .

3.  M. Novack and A. Vasseur - The Inviscid 3D Quasi-Geostrophic System on Bounded Domains - arXiv.  Arch. Rational Mech. Anal.  235 (2020), pp 973-1010) .

2.  M. Novack - On the Weak Solutions to the 3D Inviscid Quasi-Geostrophic System - arXiv.  SIAM J. Math. Anal., 51(3) (2019), 2686–2712 .

1.  M. Novack and A. Vasseur - Global in Time Classical Solutions to the 3D Quasi-Geostrophic System for Large Initial Data - arXiv.  Communications in Mathematical Physics 358 (2018) Issue 1, pp 237-267 .

Presentations and Talks

• SwissMaps Research Station - Workshop on Regularity Theory for Evolution Equations - July 2026

• U. of Pittsburgh - SIAM Annual Meeting - November 2025

• UC-Davis - PDE and Applied Math Seminar - October 2025

• Indiana University - Institute Seminar - October 2025

• Clay Research Conference - Session on PDE and Fluids - September 2025

• MCA 2025 Special Session on New Development in Fluid Dynamics - July 2025

• Sabhal Mor Ostaig Workshop on Mixing - June 2025

• Duke Analysis Seminar - April 2025

• Carnegie-Mellon CNA Seminar - April 2025

• UW-Madison Workshop on Kinetic Theory and Fluids - March 2025

• Princeton Analysis of Fluids Seminar - December 2024

• UT-Austin PDE Seminar - November 2024

• UW-Madison Workshop on Stability Analysis for Nonlinear PDEs and Multiscale Applications - November 2024

• Penn State PDE Seminar - October 2024

• KAIST Conference on New Trends in Hyperbolic Conservation Laws and Related Models - June 2024 - Intermittent Weak Solutions to the 3D Euler Equations

• Notre Dame PDE Workshop - May 2024 - Helicity Non-Conservation for the 3D Euler Equations

• AMS Spring Southeastern Sectional Meeting - March 2024 - Helicity Non-Conservation for the 3D Euler Equations 

• UIC Analysis and Applied Math Seminar - November 2023 - Weak Kinetic Shock Solutions to the Landau Equation

• Purdue PDE Seminar - November 2023 - Weak Kinetic Shock Solutions to the Landau Equation

• USC CAMS Colloquium - October 2023 - Weak Kinetic Shock Solutions to the Landau Equation

• NYU Analysis Seminar - October 2023 - The Strong Onsager Conjecture

• Simons Turbulence Seminar - August 2023 - The Strong Onsager Conjecture

• MSRI Program on Fluid Dynamics - August 2023 - The Strong Onsager Conjecture

• EPFL Summer School: Deterministic and random features of fluids - July 2023 - The Strong Onsager Conjecture

• MPI Conference on New Directions in Compressible and Incompressible Flows:  A Conference in Honor of Alexis Vasseur's 50th Birthday - June 2023 - The Strong Onsager Conjecture

• Max Planck Institute for Mathematics in the Sciences:  Lectures series on ''Anomalous Dissipation and the Strong Onsager Conjecture'' (link to YouTube recording) - June 2023

• Columbia Workshop on Free Boundary Problems:  Lecture Series and Recent Advances - June 2023 - The Strong Onsager Conjecture

• University of Basel Seminar on Analysis and Math. Physics (online) - May 2023 - The Strong Onsager Conjecture

• Chicago Calderón-Zygmund Analysis Seminar - May 2023 - The Strong Onsager Conjecture

• AMS Spring Central Sectional Meeting - May 2023 - The Strong Onsager Conjecture

• AMS Spring Central Sectional Meeting - April 2023 - The Strong Onsager Conjecture

• Texas Tech Analysis Seminar - November 2022 - Intermittent Onsager Theorems

• Purdue PDE Seminar - November 2022 - Intermittent Onsager Theorems

• Stony Brook Workshop in Small Scale Dynamics in Fluid Motion - June 2022 - An Intermittent Onsager Theorem

• CRM-Montreal Workshop on Unifying Concepts in PDEs with Randomness - May 2022 - A Forward-looking View on Convex Integration.

• Virtual Analysis and PDE Seminar - May 2022 - An Intermittent Onsager Theorem (link to YouTube recording).

• Princeton Analysis of fluids seminar - April 2022 - An Intermittent Onsager Theorem.

• Yale Analysis seminar - March 2022 - An Intermittent Onsager Theorem.

• IAS special year seminar - February 2022 - Turbulent Weak Solutions of the 3D Euler equations.

• Georgia Tech job colloquium - January 2022 - Turbulent Weak Solutions of the 3D Euler equations.

• University of Wisconsin job colloquium - December 2021 - Turbulent Weak Solutions of the 3D Euler equations.

• Purdue University job colloquium - December 2021 - Turbulent Weak Solutions of the 3D Euler equations.

• University of Maryland job colloquium - December 2021 - Turbulent Weak Solutions of the 3D Euler equations.

• UT-Austin Analysis Seminar - December 2021 - Non-conservative H1/2- weak solutions of the incompressible 3D Euler equations, 

• Cornell job colloquium - November 2021 - Turbulent Weak Solutions of the 3D Euler equations

• Texas Tech job colloquium - November 2021 - Turbulent Weak Solutions of the 3D Euler equations

• UC-Davis PDE/Applied Math Seminar - October 2021 - Non-conservative H1/2- weak solutions of the incompressible 3D Euler equations

• Drexel Applied Math Seminar - October 2021 - Non-conservative H1/2- weak solutions of the incompressible 3D Euler equations.

• Tulane Applied Math Seminar - October 2021 - Non-conservative H1/2- weak solutions of the incompressible 3D Euler equations.

• Harvard CMSA Interdisciplinary Science Seminar - April 2021 - Convex Integration and Fluid Turbulence

• AIM Workshop on Criticality and Stochasticity in Fluids - April 2021 - Convex Integration, Intermittency, and Related Topics

• MIT PDE/Analysis Seminar - March 2021 - Non-conservative H^{1/2-} weak solutions of the incompressible 3D Euler equations

• MSRI Academic Sponsors Day Short Presentation - March 2021 - Convex Integration and Turbulence

• MSRI Euler/Navier Stokes Seminar  - February 2021 - Non-conservative H^{1/2-} weak solutions of the incompressible 3D Euler equations

• UConn Analysis Seminar - September 2020 - Recent Results for the 3D Quasi-Geostrophic System

• USC Analysis Seminar - September 2020 - Recent Results for the 3D Quasi-Geostrophic System

• Mathematics of Planet Earth Webinars - June 2020 - The 3D Quasi-Geostrophic System on Bounded Domains

• Winter School: Turbulence in Fluids and PDEs - January 2020 - Convex Integration for the 3D Quasi-Geostrophic System

• Princeton University Analysis of Fluids and Related Topics Seminar - September 2019 - Recent Results on the 3D QG System: Boundary Conditions and Non-Uniqueness

• Courant Analysis Seminar - September 2019 -Recent Results on the 3D QG System: Boundary Conditions and Non-Uniqueness

• Columbia University Geometry and Analysis Seminar - April 2019 - Recent Results on the 3D QG System: Boundary Conditions and Non-Uniqueness

• Iowa State Computational and Applied Mathematics Seminar - March 2019 - Recent Results on the 3D QG System: Boundary Conditions and Non-Uniqueness

• Indiana University Analysis Seminar - Jan 2019 - Recent Results on the 3D QG System: Boundary Conditions and Non-Uniqueness

• Ki-Net Young Researchers Workshop, CSCAMM / University of Maryland - October 2018 - Recent Results on the 3D Quasi-Geostrophic System

• AMS Session, University of Michigan - October 2018 - Recent Results on the 3D Quasi-Geostrophic System

• AMS Session, Northeastern University - April 2018 - Recent Results on the 3D Quasi-Geostrophic System

• AMS Session, Portland State - April 2018 - Recent Results on the 3D Quasi-Geostrophic System

• Summer School on Mathematical Fluids, USC - May 2017 - Global Classical Solutions to the 3D Quasi-Geostrophic System