Chen, Nan; Farhat, Aseel; Lunasin, Evelyn Data assimilation with model error: analytical and computational study for Sabra shell model. (English) Zbl 1515.76087 Physica D 443, Article ID 133552, 14 p. (2023). MSC: 76F99 76M99 PDFBibTeX XMLCite \textit{N. Chen} et al., Physica D 443, Article ID 133552, 14 p. (2023; Zbl 1515.76087) Full Text: DOI
Miyajima, N.; Wirosoetisno, D. Navier-Stokes equations on the \(\beta\)-plane: determining modes and nodes. (English) Zbl 1415.76732 Physica D 386-387, 31-37 (2019). MSC: 76U05 76D05 86A05 PDFBibTeX XMLCite \textit{N. Miyajima} and \textit{D. Wirosoetisno}, Physica D 386--387, 31--37 (2019; Zbl 1415.76732) Full Text: DOI arXiv
Cheskidov, Alexey; Dai, Mimi Determining modes for the surface quasi-geostrophic equation. (English) Zbl 1398.35162 Physica D 376-377, 204-215 (2018). MSC: 35Q35 35D30 35B41 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{M. Dai}, Physica D 376--377, 204--215 (2018; Zbl 1398.35162) Full Text: DOI arXiv
Bilgin, B. A.; Kalantarov, V. K. Existence of an attractor and determining modes for structurally damped nonlinear wave equations. (English) Zbl 1398.35009 Physica D 376-377, 15-22 (2018). MSC: 35B41 35B40 37L30 35L20 PDFBibTeX XMLCite \textit{B. A. Bilgin} and \textit{V. K. Kalantarov}, Physica D 376--377, 15--22 (2018; Zbl 1398.35009) Full Text: DOI
Doering, Charles R. (ed.); Lunasin, Evelyn M. (ed.); Mazzucato, Anna (ed.) Introduction to special issue: “Nonlinear partial differential equations in mathematical fluid dynamics”. (English) Zbl 1398.00067 Physica D 376-377, 1-4 (2018). MSC: 00B15 00B30 35-06 76-06 PDFBibTeX XMLCite \textit{C. R. Doering} (ed.) et al., Physica D 376--377, 1--4 (2018; Zbl 1398.00067) Full Text: DOI
Cheskidov, Alexey; Dai, Mimi; Kavlie, Landon Determining modes for the 3D Navier-Stokes equations. (English) Zbl 1392.35205 Physica D 374-375, 1-9 (2018). MSC: 35Q30 35D30 35B41 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., Physica D 374--375, 1--9 (2018; Zbl 1392.35205) 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
Hayden, Kevin; Olson, Eric; Titi, Edriss S. Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations. (English) Zbl 1302.76048 Physica D 240, No. 18, 1416-1425 (2011). MSC: 76D03 35Q30 37N10 PDFBibTeX XMLCite \textit{K. Hayden} et al., Physica D 240, No. 18, 1416--1425 (2011; Zbl 1302.76048) Full Text: DOI arXiv
Gal, Ciprian G.; Grasselli, Maurizio Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system. (English) Zbl 1214.37055 Physica D 240, No. 7, 629-635 (2011). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37N10 37F35 76E15 76D05 PDFBibTeX XMLCite \textit{C. G. Gal} and \textit{M. Grasselli}, Physica D 240, No. 7, 629--635 (2011; Zbl 1214.37055) Full Text: DOI
Gibbon, J. D.; Holm, D. D. Length-scale estimates for the LANS-\(\alpha\) equations in terms of the Reynolds number. (English) Zbl 1331.76051 Physica D 220, No. 1, 69-78 (2006). MSC: 76F02 35Q35 37L30 37N10 PDFBibTeX XMLCite \textit{J. D. Gibbon} and \textit{D. D. Holm}, Physica D 220, No. 1, 69--78 (2006; Zbl 1331.76051) Full Text: DOI arXiv Link
Constantin, Peter; Levant, Boris; Titi, Edriss S. Analytic study of shell models of turbulence. (English) Zbl 1113.34044 Physica D 219, No. 2, 120-141 (2006). Reviewer: Marianne Reichert (Frankfurt / Main) MSC: 34G20 76D05 34A45 PDFBibTeX XMLCite \textit{P. Constantin} et al., Physica D 219, No. 2, 120--141 (2006; Zbl 1113.34044) Full Text: DOI arXiv
Kukavica, Igor; Robinson, James C. Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. (English) Zbl 1058.35045 Physica D 196, No. 1-2, 45-66 (2004). MSC: 35B41 35Q53 35Q30 PDFBibTeX XMLCite \textit{I. Kukavica} and \textit{J. C. Robinson}, Physica D 196, No. 1--2, 45--66 (2004; Zbl 1058.35045) Full Text: DOI
Robinson, James C. Low dimensional attractors arise from forcing at small scales. (English) Zbl 1040.35063 Physica D 181, No. 1-2, 39-44 (2003). MSC: 35Q30 37L30 76D05 PDFBibTeX XMLCite \textit{J. C. Robinson}, Physica D 181, No. 1--2, 39--44 (2003; Zbl 1040.35063) Full Text: DOI
Doering, Charles R.; Gibbon, J. D. Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations. (English) Zbl 0997.35046 Physica D 165, No. 3-4, 163-175 (2002). MSC: 35Q30 76F60 76D05 PDFBibTeX XMLCite \textit{C. R. Doering} and \textit{J. D. Gibbon}, Physica D 165, No. 3--4, 163--175 (2002; Zbl 0997.35046) Full Text: DOI
Groves, M. D. An existence theory for three-dimensional periodic travelling gravity-capillary water waves with bounded transverse profiles. (English) Zbl 1037.76005 Physica D 152-153, 395-415 (2001). MSC: 76B15 76B45 35Q35 37N10 PDFBibTeX XMLCite \textit{M. D. Groves}, Physica D 152--153, 395--415 (2001; Zbl 1037.76005) Full Text: DOI
Gibbon, J. D. A voyage around the Navier-Stokes equations. (English) Zbl 1031.76516 Physica D 92, No. 3-4, 133-139 (1996). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{J. D. Gibbon}, Physica D 92, No. 3--4, 133--139 (1996; Zbl 1031.76516) Full Text: DOI
Jones, Don A.; Titi, Edriss S. Determining finite volume elements for the 2D Navier-Stokes equations. (English) Zbl 0778.35084 Physica D 60, No. 1-4, 165-174 (1992). MSC: 35Q30 35B40 PDFBibTeX XMLCite \textit{D. A. Jones} and \textit{E. S. Titi}, Physica D 60, No. 1--4, 165--174 (1992; Zbl 0778.35084) Full Text: DOI
Lions, P. L. Asymptotic behavior of some nonlinear heat equations. (English) Zbl 1194.35459 Physica D 5, No. 2-3, 293-306 (1982). MSC: 35Q79 PDFBibTeX XMLCite \textit{P. L. Lions}, Physica D 5, No. 2--3, 293--306 (1982; Zbl 1194.35459) Full Text: DOI