Publications of Nathan Glatt-Holtz:

Google Scholar Page

[43] “Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier-Stokes equations as a paradigm” (with C. Mondaini), (preprint)

[42] “The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction.” (with V. Martinez and H. Nguyen), (preprint)

[41] “Unique Ergodicity in Stochastic Electroconvection” (with E. Abdo and M. Ignatova), (preprint)

[40] “Parallel MCMC Algorithms: Theoretical Foundations, Algorithm Design, Case Studies” (with C. Mondaini, A. Holbrook and J. Krometis), (preprint)

[39] "On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically- driven KdV equation” (with V. Martinez and G. Richards), (preprint)

[38] “Embracing Uncertainty in ”Small Data” Problems: Estimating Earthquakes from Historical Anecdotes” (with J. Krometis, R. Harris, H. Ringer and J. Whitehead), (preprint)

[37] “Hydrodynamic stability in the presence of a stochastic forcing: a case study in convection'' (with J. Földes, G. Richards, and J. Whitehead), (preprint)

[36] “A Statistical Framework for Domain Shape Estimation in Stokes Flows” (with J.Borggaard and J. Krometis).
        Inverse Problems (preprint) (journal-- to appear).

[35] “On the accept-reject mechanism for Metropolis-Hastings algorithms" (with C. Mondaini and J. Krometis),
        Annals of Applied Probability (preprint) (journal-- to appear)

 [34] “Mixing Rates for Hamiltonian Monte Carlo Algorithms in Finite and Infinite Dimensions" (with C. Mondaini),
        Stochastics and Partial Differential Equations: Analysis and Computations, 2021 (preprint) (journal)
 
[33] “Sensitivity of steady states in a degenerately-damped stochastic Lorenz system" (with J. Földes, D. Herzog),
        Stochastics and Dynamics, 2021 (preprint) (journal)

[32] “Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis:
            a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami”
        (with H. Ringer, J. Whitehead, J. Krometis, R. Harris, S. Giddens, C. Ashcraft, G. Carver, A. Robertson, M. Harward,
            J. Fullwood, K. Lightheart, R. Hilton, A. Avery, C. Kesler, M. Morrise, M. Klein).
        JGR: Solid Earth, Volume 126, Issue 4, April 2021. (preprint) (journal)

[31] “A Bayesian Approach to Estimating Background Flows from a Passive Scalar" (with J.Borggaard and J. Krometis)
        SIAM/ASA Journal on Uncertainty Quantification, 8(3):1036– 1060, 2020. (preprint) (journal)

[30] “On Bayesian Consistency for Flows Observed Through a Passive Scalar'' (with J.Borggaard and J. Krometis).
        Annals of Applied Probability, 30(4):1762–1783. (preprint) (journal)

[29] “The Generalized Langevin Equation with power-law memory in a non-linear potential well'' (with D. Herzog, S. McKinley, H. Nguyen)
        Nonlinearity (2020) Volume 33, Number 6. (preprint) (journal).

[28] “Data Assimilation in Large-Prandtl Rayleigh-Bénard Convection from Thermal Measurements'' (with A. Farhat, N. Glatt-Holtz, V. Martinez, S. McQuarrie, J. Whitehead)
        SIAM Journal on Applied Dynamical Systems. (2019) (1), 510–540. (preprint) (journal)
 
[27] “On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems'' (with S. Cerrai)
        Journal of Functional Analysis. (2019) 108421. (preprint) (journal)

 [26] “GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems'' (with J.Borggaard and J. Krometis).
        Journal of Computational Physics 391 (2019): 142-154. (preprint) (journal)

[25] “Invariant measures for the stochastic one-dimensional compressible Navier-Stokes equations'' (with M. Coti Zelati, N. Glatt-Holtz, and K. Trivisa).
        Appl Math Optim (2019) (preprint) (journal)

[24] “Large Prandtl Number Asymptotics in Randomly Forced Turbulent Convection" (with J. Földes and G. Richards). 
        Nonlinear Differ. Equ. Appl. (2019) 26: 43. (preprint) (journal)

[23] “Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations'' (with D. Herzog, J. C. Mattingly).
        Annals of PDE.  (2018) 4: 16. (preprint) (journal)

[22]  “Asymptotic Analysis for Randomly Forced MHD" (with J. Földes, S. Friedlander, G. Richards).
        SIAM J. Math. Anal., 49(6), 4440–4469, 2017. (preprint) (journal)

[21] “On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations" (with J. C. Mattingly, G. Richards).
        J. Stat Phys, 1--32, 2016. (preprint) (journal)

[20] “Ergodicity in Randomly Forced Rayleigh-Benard Convection" (with J. Foldes, G. Richards, J.P. Whitehead)
        Nonlinearity, Nov 2016, Volume 29, Number 11. (preprint) (journal)

[19] “Invariant measures for passive scalars in the small noise inviscid limit'' (with J. Bedrossian and M. Coti Zelati).
        Comm. Math. Phys., Nov 2016, Volume 348, Issue 1, pp 101--127. (preprint) (journal)

[18] “Time Discrete Approximation of Weak Solutions for Stochastic Equations of Geophysical Fluid Dynamics and Applications" (with R. Temam and C. Wang)       
        Chinese Annals of Mathematics Ser. B 38 2017, no.2,  425--472.  (preprint) (journal)

[17] “Inviscid Limits for a Stochastically Forced Shell Model of Turbulent Flow” (with S. Friedlander and V. Vicol)
        Annales de l’Institut Henri Poincare, Probabilites et Statistiques, Volume 52, Number 3 (2016), 1217-1247. (preprint) (journal)

[16] “Ergodic and Mixing Properties of The Boussinesq Equations with a Degenerate Random Forcing'' (with J. Földes, G. Richards and E. Thomann)
        Journal of Functional Analysis,Volume 269, Issue 8, 15 October 2015, Pages 2427–2504. (preprint) (journal)

[15]  “Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise" (with R. Temam and C. Wang)
        Discrete Contin. Dyn. Syst. Ser. B., 19 (2014), no. 4, 1047-1085. (preprint) (journal)

[14] “Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations" (with I. Kukavica, V. Vicol and M. Ziane)
        J. Math. Phys. 55, 051504 (2014). (preprint) (journal)

[13] “Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations" (with P. Constantin and V. Vicol)
        Communications in Mathematical Physics, September 2014, Volume 330, Issue 2, pp 819-857. (preprint) (journal)

[12] “On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models" (with V.  Sverak and V. Vicol)
        Archive for Rational Mechanics and Analysis, Volume 217, Issue 2 (2015), pp 619-649. (preprint) (journal)

[11] “Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise" (with V. Vicol)
        Annals of Probability, Volume 42, Number 1 (2014), 1-430. (preprint) (journal)

[10] “Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications" (with M. Chekroun)
        Communications in Mathematical Physics  vol 316, 723-761 2012. (preprint) (journal)

[9] “Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise'' 
        (with A. Debussche,  R. Temam and M. Ziane)
        Nonlinearity, vol 316, 723-761 2012. (preprint) (journal)

[8] “Local Martingale and Pathwise Solutions for an Abstract Fluids Model'' (with A. Debussche and  R. Temam)
        Physica D vol 240, Issues 14-15, 15 July 2011, pp. 1123-1144. (preprint) (journal)

[7] “Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations'' (with I. Cialenco)
        Stochastic Processes and their Applications, vol 121, pp. 701-724, 2011. (preprint) (journal)

[6] “Pathwise Solutions of the 2-D Stochastic Primitive Equations'' (with R. Temam) 
        Applied Mathematics and Optimization Vol 63, No 3, 401-433. (preprint) (journal)
 
[5] “Cauchy Convergence Schemes for Some Nonlinear Partial Differential Equations'' (with R. Temam)
        Applicable Analysis--Special Issue in honor of Prof. V. Solonnikov, Vol 90, No 1, 2011, 85 - 102. (preprint) (journal)

[4] “Asymptotics of the Coleman-Gurtin model'' (with M. Chekroun, F. Di Plinio, and V. Pata)
        Discrete Contin. Dyn. Syst. Ser. S (Vol. 4, No. 2) April 2011. (preprint) (journal)

[3] “Singular Perturbation Systems with Stochastic Forcing and the Renormalization Group Method'' (with M. Ziane) 
        Discrete Contin. Dyn. Syst. Ser. A (2010), Vol 26, No 4, 1241–1268. (preprint) (journal)

[2] “Strong Pathwise Solutions of the Stochastic Navier-Stokes System'' (with M. Ziane) 
        Adv. Differential Equations – 14 (2009), no. 5-6, 567-600. (preprint) (journal)

[1] “The Stochastic Primitive Equations in Two Space Dimensions with Multiplicative Noise'' (with M. Ziane)
        Discrete Contin. Dyn. Syst. Ser. B (2008), Vol 10, No. 4,  801–822. (preprint) (journal)





"Well Posedness and Asymptotic Analysis for the Stochastic Equations of Geophysical Fluid Dynamics" - Ph.D Thesis, University of Southern California (August, 2008)



Expository

[1] Notes on Statistically Invariant States in Stochastically Driven Fluid Flows (preprint)