Carlson, Elizabeth; Hudson, Joshua; Larios, Adam; Martinez, Vincent R.; Ng, Eunice; Whitehead, Jared P. Dynamically learning the parameters of a chaotic system using partial observations. (English) Zbl 1502.37092 Discrete Contin. Dyn. Syst. 42, No. 8, 3809-3839 (2022). MSC: 37M99 68T05 PDFBibTeX XMLCite \textit{E. Carlson} et al., Discrete Contin. Dyn. Syst. 42, No. 8, 3809--3839 (2022; Zbl 1502.37092) Full Text: DOI arXiv
Martinez, Vincent R. Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier-Stokes equations. (English) Zbl 1487.35300 Nonlinearity 35, No. 5, 2241-2287 (2022). MSC: 35Q30 76D05 76D55 35B30 93B30 93B52 PDFBibTeX XMLCite \textit{V. R. Martinez}, Nonlinearity 35, No. 5, 2241--2287 (2022; Zbl 1487.35300) Full Text: DOI arXiv
Jolly, Michael S.; Kumar, Anuj; Martinez, Vincent R. On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces. (English) Zbl 1479.35866 Commun. Math. Phys. 387, No. 1, 551-596 (2021). MSC: 35Q86 35Q35 76U60 35B65 35K59 35A01 35A02 86A05 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Commun. Math. Phys. 387, No. 1, 551--596 (2021; Zbl 1479.35866) Full Text: DOI arXiv
Farhat, A.; Glatt-Holtz, N. E.; Martinez, V. R.; McQuarrie, S. A.; Whitehead, J. P. Data assimilation in large Prandtl Rayleigh-Bénard convection from thermal measurements. (English) Zbl 1434.76041 SIAM J. Appl. Dyn. Syst. 19, No. 1, 510-540 (2020). MSC: 76E06 62M20 35Q35 76-10 62P35 PDFBibTeX XMLCite \textit{A. Farhat} et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 510--540 (2020; Zbl 1434.76041) Full Text: DOI arXiv
Jolly, Michael S.; Martinez, Vincent R.; Olson, Eric J.; Titi, Edriss S. Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation. (English) Zbl 1427.35204 Chin. Ann. Math., Ser. B 40, No. 5, 721-764 (2019). MSC: 35Q35 35Q86 35Q93 37B55 93B52 35B40 76W05 86A10 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Chin. Ann. Math., Ser. B 40, No. 5, 721--764 (2019; Zbl 1427.35204) Full Text: DOI arXiv
Jolly, Michael S.; Martinez, Vincent R.; Sadigov, Tural; Titi, Edriss S. A determining form for the subcritical surface quasi-geostrophic equation. (English) Zbl 1420.35042 J. Dyn. Differ. Equations 31, No. 3, 1457-1494 (2019). MSC: 35B40 35R11 35Q35 35Q86 35G25 35B10 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., J. Dyn. Differ. Equations 31, No. 3, 1457--1494 (2019; Zbl 1420.35042) Full Text: DOI arXiv
Blocher, Jordan; Martinez, Vincent R.; Olson, Eric Data assimilation using noisy time-averaged measurements. (English) Zbl 1398.93119 Physica D 376-377, 49-59 (2018). MSC: 93B52 34D05 34H10 34K50 93E14 93C23 PDFBibTeX XMLCite \textit{J. Blocher} et al., Physica D 376--377, 49--59 (2018; Zbl 1398.93119) Full Text: DOI
Hoang, Luan T.; Martinez, Vincent R. Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forces. (English) Zbl 1394.35130 J. Math. Anal. Appl. 462, No. 1, 84-113 (2018). MSC: 35C20 35Q30 76D05 PDFBibTeX XMLCite \textit{L. T. Hoang} and \textit{V. R. Martinez}, J. Math. Anal. Appl. 462, No. 1, 84--113 (2018; Zbl 1394.35130) Full Text: DOI arXiv
Jolly, Michael S.; Martinez, Vincent R.; Titi, Edriss S. A data assimilation algorithm for the subcritical surface quasi-geostrophic equation. (English) Zbl 1358.35091 Adv. Nonlinear Stud. 17, No. 1, 167-192 (2017). MSC: 35Q30 37C50 76B75 34D06 35Q86 42B25 26A33 76B15 76U05 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Adv. Nonlinear Stud. 17, No. 1, 167--192 (2017; Zbl 1358.35091) Full Text: DOI arXiv
Biswas, Animikh; Martinez, Vincent R. Higher-order synchronization for a data assimilation algorithm for the 2D Navier-Stokes equations. (English) Zbl 1359.35124 Nonlinear Anal., Real World Appl. 35, 132-157 (2017). MSC: 35Q30 76B75 93C20 PDFBibTeX XMLCite \textit{A. Biswas} and \textit{V. R. Martinez}, Nonlinear Anal., Real World Appl. 35, 132--157 (2017; Zbl 1359.35124) Full Text: DOI
Biswas, Animikh; Martinez, Vincent R.; Silva, Prabath On Gevrey regularity of the supercritical SQG equation in critical Besov spaces. (English) Zbl 1329.35090 J. Funct. Anal. 269, No. 10, 3083-3119 (2015). MSC: 35B65 PDFBibTeX XMLCite \textit{A. Biswas} et al., J. Funct. Anal. 269, No. 10, 3083--3119 (2015; Zbl 1329.35090) Full Text: DOI arXiv
Biswas, A.; Jolly, M. S.; Martinez, V. R.; Titi, E. S. Dissipation length scale estimates for turbulent flows: a Wiener algebra approach. (English) Zbl 1300.35066 J. Nonlinear Sci. 24, No. 3, 441-471 (2014). MSC: 35Q30 76F02 76D05 PDFBibTeX XMLCite \textit{A. Biswas} et al., J. Nonlinear Sci. 24, No. 3, 441--471 (2014; Zbl 1300.35066) Full Text: DOI arXiv