Eric Olson

Department of Mathematics/084
University of Nevada, Reno
Reno, NV 89557
email: ejolson at unr.edu

Publications

  1. with C. Foias, Finite fractal dimension and Hölder-Lipschitz parametrization. Indiana Univ. Math. J. 45 (1996), no. 3, 603--616. (ps)

  2. with S. Chen, C. Foias, D.D. Holm, E.S. Titi and S. Wynne, Camassa-Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett. 81 (1998), no. 24, 5338--5341. (ps)

  3. with S. Chen, C. Foias, D.D. Holm, E.S. Titi and S. Wynne, A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. The International Conference on Turbulence (Los Alamos, NM, 1998), Phys. Fluids 11 (1999), no. 8, 2343--2353. (ps)

  4. with S. Chen, C. Foias, D.D. Holm, E.S. Titi and S. Wynne, The Camassa-Holm equations and turbulence. Predictability: quantifying uncertainty in models of complex phenomena (Los Alamos, NM, 1998). Phys. D 133 (1999), no. 1-4, 49--65. (ps)

  5. Bouligand dimension and almost Lipschitz embeddings, Pacific J. Math. 202 (2002), no. 2, 459--474. (ps, errata)

  6. with E.S. Titi, Determining modes for continuous data assimilation in 2D turbulence. Progress in statistical hydrodynamics (Santa Fe, NM, 2002), J. Statist. Phys. 113 (2003), no. 5-6, 799--840. (ps, pdf)

  7. with A. Cheskidov, D.D. Holm,and E.S. Titi, On a Leray-alpha Model of Turbulence, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), no. 2055, 629--649. (ps)

  8. with Ciprian Foias, Luan Hoang and Mohammed Ziane, On the Solutions to the Normal Form of the Navier--Stokes Equations, Indiana Univ. Math. Journal 55:2 (2006), 631--686. (ps)

  9. with E.S. Titi, Viscosity Versus Vorticity Stretching: Global Well-posedness for a Family of Navier--Stokes-Alpha-like Models, Nonlinear Analysis, 66 (2007), no. 11, 2427--2458. (ps)

  10. with E.S. Titi, Determining Modes and Grashof Number in 2D Turbulence---A Numerical Case Study, Theoretical and Computational Fluid Dynamics, Vol. 22, No. 5, 2008, pp. 327--339. (pdf)

  11. with Ciprian Foias, Luan Hoang and Mohammed Ziane, The Normal Form of the Navier--Stokes Equations in Suitable Normed Spaces, Ann. Inst. H. Poincaré Anal. Non Lin\'eaire 26 (2009), no. 5, 1635--1673. (ps)

  12. with James Robinson, Almost Bi-Lipshitz Embeddings and Almost Homogeneous Sets, Trans. Amer. Math. Soc. (2010), no. 1, 145--168. (ps)

  13. with Kevin Hayden and Edriss Titi, Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations Physica D: Nonlinear Phenomena, Volume 240, Issue 18, 1 September 2011, pp. 1416--1425. (pdf)

  14. with Abderrahim Azouani and Edriss Titi, Continuous Data Assimilation Using General Interpolant Observables, Journal of Nonlinear Science, Volume 24, April 2014, pp. 277--304. (pdf, errata)

  15. with Hakima Bessaih and Edriss Titi, Continuous Data Assimilation with Stochastically Noisy Data, Nonlinearity, Volume 28, 2015, pp. 729--753. (pdf)

  16. with Jonathan Fraser, Alexander Henderson and James Robinson, On the Assouad Dimension of Self-similar Sets with Overlaps, Advances in Mathematics, Volume 273, 2015, pp. 181--214. (pdf)

  17. with Luan Hoang and James Robinson, On the Continuity of Global Attractors, Proceedings of the American Mathematical Society, Volume 143, 2015, no. 10, pp. 4389--4395. (pdf)

  18. with James Robinson and Nicholas Sharples, Generalised Cantor Sets and the Dimension of Products, to appear in Mathematical Proceedings of the Cambridge Philosophical Society, Volume 160, 2016, no. 1, pp. 51--75. (pdf)

  19. with James Robinson, A Simple Example Concerning the Upper Box-counting Dimension of a Cartesian Product, Real Analysis Exchange, Volume 40.2, 2016, pp. 449--452. (pdf)

  20. with Masakazu Gesho and Edriss Titi, A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier--Stokes Equations, Communications in Computational Physics, Volume 19, no. 4, pp. 1094--1110, 2016. (pdf)

  21. with David McCormick, James Robinson, Jose Rodrigo, Vidal-Lopez and Yi Zhou, Lower bounds on blowing-up solutions of the 3D Navier-Stokes equations in H3/2, H5/2 and B2,15/2, SIAM Journal on Mathematical Analysis, Vol. 48, No. 3, 2016, pp. 2119-2132. (pdf)

  22. with Jonathan Fraser and James Robinson, Some Results in Support of the Kakeya Conjecture, Real Analysis Exchange, Vol. 42, No. 2, 2017, pp. 253-268. (pdf)

  23. with Jordan Blocher and Vincent Martinez, Data Assimilation Using Noisy Time-Averaged Measurements, Physica D, Volumes 376--377, pp 49-59, August 2018 (pdf).

  24. with Luan Hoang and James Robinson, Continuity of Pullback and Uniform Attractors, Journal of Differential Equations, Vol 264, Issue 6, 15 March 2018, pp 4067-4093 (pdf).

  25. Stochastic model error in the LANS-alpha and NS-alpha deconvolution models of turbulence, International Journal of Numerical Analysis & Modeling, No. 6, pp. 811-833, 2018 (pdf).

  26. with Emine Celik and Edriss Titi, Spectral Filtering of Interpolant Observables for Discrete-in-time Data Assimilation, SIAM Journal on Applied Dynamical Systems, Vol 18, No 2, 2019, pp 1118-1142. (pdf).

  27. with Mike Jolly, Vincent Martinez and Edriss Titi, Continuous Data Assimilation with Blurred-in-time Measurements of the Surface Quasi-geostrophic Equation, Chinese Annals of Mathematics, Ser B, Vol 40, No 2, 2019, pp. 721-764 (pdf).

  28. with Tahj Hill, Monika Neda and Fran Pahlevani, Energy and Enstrophy Study of the Time-Relaxation Model, International Journal of Numerical Analysis and Modeling, Vol 18, No 2, 2021, pp. 165-189 (pdf).

  29. Stochastic Parameterization of the Time-Relaxation Model of Turbulence, Results in Applied Mathematics, Vol 8, 2020, 17 pages (pdf).

  30. with Alexey Cheskidov and Beau Smith, Symmetry-breaking perturbations on the global attractor of the Kuramoto-Sivashinsky equation, Pure and Applied Functional Analysis, Vol 7, No 1, 2022, pp 145-173 (pdf).

  31. with Emine Celik, Data Assimilation using Time-Delay Nudging in the Presence of Gaussian Noise, Journal of Nonlinear Science, Vol 33, Article 110, 2023, 31 pages (pdf).

  32. with Alexander Henderson, James Robinson and Nicholas Sharples, Equi-homogeneity, Assouad Dimension and Non-autonomous Dynamics, under revision (pdf).

  33. with Alexandros Margaris and James Robinson, On the Assouad dimensionof differences of self-similar fractals, submitted.