Carlson, Elizabeth; Larios, Adam; Titi, Edriss S. Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: the 2D Navier-Stokes equation paradigm. (English) Zbl 07812573 J. Nonlinear Sci. 34, No. 2, Paper No. 37, 41 p. (2024). MSC: 35K61 35Q93 93C20 PDFBibTeX XMLCite \textit{E. Carlson} et al., J. Nonlinear Sci. 34, No. 2, Paper No. 37, 41 p. (2024; Zbl 07812573) Full Text: DOI arXiv
Liu, Xin; Titi, Edriss S. Local well-posedness of strong solutions to the three-dimensional compressible primitive equations. (English) Zbl 1472.35393 Arch. Ration. Mech. Anal. 241, No. 2, 729-764 (2021). MSC: 35Q86 86A10 76N10 35B30 35B45 35A01 35A02 35D35 PDFBibTeX XMLCite \textit{X. Liu} and \textit{E. S. Titi}, Arch. Ration. Mech. Anal. 241, No. 2, 729--764 (2021; Zbl 1472.35393) Full Text: DOI arXiv
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity. (English) Zbl 1484.35315 Physica D 412, Article ID 132606, 25 p. (2020). MSC: 35Q35 35B30 35Q86 76D03 86A05 86A10 PDFBibTeX XMLCite \textit{C. Cao} et al., Physica D 412, Article ID 132606, 25 p. (2020; Zbl 1484.35315) Full Text: DOI arXiv
Ibdah, Hussain A.; Mondaini, Cecilia F.; Titi, Edriss S. Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates. (English) Zbl 1466.65154 IMA J. Numer. Anal. 40, No. 4, 2584-2625 (2020). MSC: 65M70 65M60 65M06 65M12 65M15 93B52 76D05 35Q30 PDFBibTeX XMLCite \textit{H. A. Ibdah} et al., IMA J. Numer. Anal. 40, No. 4, 2584--2625 (2020; Zbl 1466.65154) Full Text: DOI
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the Navier-Stokes equations. (English) Zbl 1448.65157 SIAM J. Numer. Anal. 58, No. 1, 410-429 (2020). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 65M60 65M12 35Q30 65M15 65M20 76B75 65N30 65M70 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., SIAM J. Numer. Anal. 58, No. 1, 410--429 (2020; Zbl 1448.65157) Full Text: DOI arXiv
Mondaini, Cecilia F.; Titi, Edriss S. Uniform-in-time error estimates for the postprocessing Galerkin method applied to a data assimilation algorithm. (English) Zbl 1384.35067 SIAM J. Numer. Anal. 56, No. 1, 78-110 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 76B75 37L65 65M15 65M60 65M70 93C20 93B52 PDFBibTeX XMLCite \textit{C. F. Mondaini} and \textit{E. S. Titi}, SIAM J. Numer. Anal. 56, No. 1, 78--110 (2018; Zbl 1384.35067) Full Text: DOI
Altaf, M. U.; Titi, E. S.; Gebrael, T.; Knio, O. M.; Zhao, L.; McCabe, M. F.; Hoteit, I. Downscaling the 2D Bénard convection equations using continuous data assimilation. (English) Zbl 1383.65088 Comput. Geosci. 21, No. 3, 393-410 (2017). MSC: 65M06 65M55 76R10 76M20 35K55 PDFBibTeX XMLCite \textit{M. U. Altaf} et al., Comput. Geosci. 21, No. 3, 393--410 (2017; Zbl 1383.65088) Full Text: DOI arXiv
Li, Jinkai; Titi, Edriss S. Existence and uniqueness of weak solutions to viscous primitive equations for a certain class of discontinuous initial data. (English) Zbl 1364.35275 SIAM J. Math. Anal. 49, No. 1, 1-28 (2017). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q35 76D03 76D05 86A10 35D30 PDFBibTeX XMLCite \textit{J. Li} and \textit{E. S. Titi}, SIAM J. Math. Anal. 49, No. 1, 1--28 (2017; Zbl 1364.35275) Full Text: DOI arXiv
Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. (English) Zbl 1351.35125 Commun. Pure Appl. Math. 69, No. 8, 1492-1531 (2016). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 76N10 35B30 35Q86 86A05 86A10 35D35 PDFBibTeX XMLCite \textit{C. Cao} et al., Commun. Pure Appl. Math. 69, No. 8, 1492--1531 (2016; Zbl 1351.35125) Full Text: DOI arXiv Link
Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements. (English) Zbl 1334.35230 J. Math. Anal. Appl. 438, No. 1, 492-506 (2016). MSC: 35Q35 76R10 35B45 76M12 65M08 76S05 93B52 PDFBibTeX XMLCite \textit{A. Farhat} et al., J. Math. Anal. Appl. 438, No. 1, 492--506 (2016; Zbl 1334.35230) Full Text: DOI arXiv
Farhat, Aseel; Jolly, Michael S.; Titi, Edriss S. Continuous data assimilation for the 2D Bénard convection through velocity measurements alone. (English) Zbl 1364.76053 Physica D 303, 59-66 (2015). MSC: 76E06 35B30 35Q35 35B41 PDFBibTeX XMLCite \textit{A. Farhat} et al., Physica D 303, 59--66 (2015; Zbl 1364.76053) Full Text: DOI arXiv
Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S. On the radius of analyticity of solutions to the cubic Szegő equation. (English) Zbl 1332.35058 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 1, 97-108 (2015). MSC: 35B65 35B10 47B35 35Q55 PDFBibTeX XMLCite \textit{P. Gérard} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 1, 97--108 (2015; Zbl 1332.35058) Full Text: DOI arXiv
Cao, Chongsheng; Farhat, Aseel; Titi, Edriss S. Global well-posedness of an inviscid three-dimensional pseudo-Hasegawa-Mima model. (English) Zbl 1308.35200 Commun. Math. Phys. 319, No. 1, 195-229 (2013). MSC: 35Q35 76X05 35B30 86A05 PDFBibTeX XMLCite \textit{C. Cao} et al., Commun. Math. Phys. 319, No. 1, 195--229 (2013; Zbl 1308.35200) Full Text: DOI arXiv
Babin, Anatoli V.; Ilyin, Alexei A.; Titi, Edriss S. On the regularization mechanism for the periodic Korteweg-de Vries equation. (English) Zbl 1284.35365 Commun. Pure Appl. Math. 64, No. 5, 591-648 (2011). MSC: 35Q53 35A35 35B30 PDFBibTeX XMLCite \textit{A. V. Babin} et al., Commun. Pure Appl. Math. 64, No. 5, 591--648 (2011; Zbl 1284.35365) Full Text: DOI arXiv
Oliver, Marcel; Titi, Edriss S. Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a porous medium. (English) Zbl 0949.35025 J. Differ. Equations 163, No. 2, 292-311 (2000). Reviewer: Valeriu Al.Sava (Iaşi) MSC: 35B65 35B41 35Q35 76R10 76S05 PDFBibTeX XMLCite \textit{M. Oliver} and \textit{E. S. Titi}, J. Differ. Equations 163, No. 2, 292--311 (2000; Zbl 0949.35025) Full Text: DOI
Levermore, C. David; Oliver, Marcel; Titi, Edriss S. Global well-posedness for models of shallow water in a basin with a varying bottom. (English) Zbl 0953.76011 Indiana Univ. Math. J. 45, No. 2, 479-510 (1996). MSC: 76B15 35Q35 35B30 PDFBibTeX XMLCite \textit{C. D. Levermore} et al., Indiana Univ. Math. J. 45, No. 2, 479--510 (1996; Zbl 0953.76011) Full Text: DOI