Crisan, Dan; Holm, Darryl D.; Leahy, James-Michael; Nilssen, Torstein Variational principles for fluid dynamics on rough paths. (English) Zbl 1495.35145 Adv. Math. 404, Part A, Article ID 108409, 75 p. (2022). Reviewer: Cheng He (Beijing) MSC: 35Q35 37K58 60H15 60L20 60L50 60G22 PDFBibTeX XMLCite \textit{D. Crisan} et al., Adv. Math. 404, Part A, Article ID 108409, 75 p. (2022; Zbl 1495.35145) Full Text: DOI arXiv
Drivas, Theodore D.; Holm, Darryl D. Circulation and energy theorem preserving stochastic fluids. (English) Zbl 1464.76023 Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 6, 2776-2814 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 76D06 76B03 76M35 35Q30 35Q31 PDFBibTeX XMLCite \textit{T. D. Drivas} and \textit{D. D. Holm}, Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 6, 2776--2814 (2020; Zbl 1464.76023) Full Text: DOI arXiv
Drivas, Theodore D.; Holm, Darryl D.; Leahy, James-Michael Lagrangian averaged stochastic advection by Lie transport for fluids. (English) Zbl 1471.76024 J. Stat. Phys. 179, No. 5-6, 1304-1342 (2020). MSC: 76D06 76M35 35Q30 60H15 PDFBibTeX XMLCite \textit{T. D. Drivas} et al., J. Stat. Phys. 179, No. 5--6, 1304--1342 (2020; Zbl 1471.76024) Full Text: DOI arXiv
Bethencourt de Léon, Aythami; Holm, Darryl D.; Luesink, Erwin; Takao, So Implications of Kunita-Itô-Wentzell formula for \(k\)-forms in stochastic fluid dynamics. (English) Zbl 1448.70059 J. Nonlinear Sci. 30, No. 4, 1421-1454 (2020). MSC: 70L10 70H25 70H33 70S05 70S10 70S20 76M35 60H15 PDFBibTeX XMLCite \textit{A. Bethencourt de Léon} et al., J. Nonlinear Sci. 30, No. 4, 1421--1454 (2020; Zbl 1448.70059) Full Text: DOI arXiv
Gay-Balmaz, François; Holm, Darryl D. Predicting uncertainty in geometric fluid mechanics. (English) Zbl 1439.49083 Discrete Contin. Dyn. Syst., Ser. S 13, No. 4, 1229-1242 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 49S05 70H25 76M30 49J55 PDFBibTeX XMLCite \textit{F. Gay-Balmaz} and \textit{D. D. Holm}, Discrete Contin. Dyn. Syst., Ser. S 13, No. 4, 1229--1242 (2020; Zbl 1439.49083) Full Text: DOI arXiv
Gay-Balmaz, François; Holm, Darryl D. Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows. (English) Zbl 1431.37068 J. Nonlinear Sci. 28, No. 3, 873-904 (2018). Reviewer: Božidar Jovanović (Beograd) MSC: 37N10 37K25 37H10 60H15 70G45 86A05 PDFBibTeX XMLCite \textit{F. Gay-Balmaz} and \textit{D. D. Holm}, J. Nonlinear Sci. 28, No. 3, 873--904 (2018; Zbl 1431.37068) Full Text: DOI arXiv Link
Holm, Darryl D.; Jacobs, Henry O. Multipole vortex blobs (MVB): symplectic geometry and dynamics. (English) Zbl 1365.76212 J. Nonlinear Sci. 27, No. 3, 973-1006 (2017). MSC: 76M23 76M60 70H15 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{H. O. Jacobs}, J. Nonlinear Sci. 27, No. 3, 973--1006 (2017; Zbl 1365.76212) Full Text: DOI arXiv Link
Cotter, C. J.; Eldering, J.; Holm, D. D.; Jacobs, H. O.; Meier, D. M. Weak dual pairs and jetlet methods for ideal incompressible fluid models in \(n \geq 2\) dimensions. (English) Zbl 1368.37076 J. Nonlinear Sci. 26, No. 6, 1723-1765 (2016). Reviewer: Kai Schneider (Marseille) MSC: 37K05 35Q35 65P10 76B10 PDFBibTeX XMLCite \textit{C. J. Cotter} et al., J. Nonlinear Sci. 26, No. 6, 1723--1765 (2016; Zbl 1368.37076) Full Text: DOI arXiv
Cotter, C. J.; Holm, D. D. On Noether’s theorem for the Euler-Poincaré equation on the diffeomorphism group with advected quantities. (English) Zbl 1352.37173 Found. Comput. Math. 13, No. 4, 457-477 (2013). Reviewer: Oleg V. Makeev (Ulyanovsk) MSC: 37K05 76M60 PDFBibTeX XMLCite \textit{C. J. Cotter} and \textit{D. D. Holm}, Found. Comput. Math. 13, No. 4, 457--477 (2013; Zbl 1352.37173) Full Text: DOI arXiv
Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier Invariant higher-order variational problems. II. (English) Zbl 1351.58009 J. Nonlinear Sci. 22, No. 4, 553-597 (2012). MSC: 58E05 49J27 58D19 70H25 70H30 70H45 70H50 PDFBibTeX XMLCite \textit{F. Gay-Balmaz} et al., J. Nonlinear Sci. 22, No. 4, 553--597 (2012; Zbl 1351.58009) Full Text: DOI arXiv
Holm, Darryl D.; Ivanov, Rossen I.; Percival, James R. \(G\)-strands. (English) Zbl 1339.37048 J. Nonlinear Sci. 22, No. 4, 517-551 (2012). MSC: 37K05 37K65 70H25 70H03 37M05 PDFBibTeX XMLCite \textit{D. D. Holm} et al., J. Nonlinear Sci. 22, No. 4, 517--551 (2012; Zbl 1339.37048) Full Text: DOI arXiv
Holm, Darryl D.; Putkaradze, Vakhtang; Tronci, Cesare Geometric gradient-flow dynamics with singular solutions. (English) Zbl 1155.76007 Physica D 237, No. 22, 2952-2965 (2008). MSC: 76D03 37K65 35L65 37N10 70F99 82C22 PDFBibTeX XMLCite \textit{D. D. Holm} et al., Physica D 237, No. 22, 2952--2965 (2008; Zbl 1155.76007) Full Text: DOI arXiv
Holm, Darryl D. Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics. (English) Zbl 1080.76504 Chaos 12, No. 2, 518-530 (2002). MSC: 76A02 76F99 76W05 PDFBibTeX XMLCite \textit{D. D. Holm}, Chaos 12, No. 2, 518--530 (2002; Zbl 1080.76504) Full Text: DOI
Holm, Darryl D. Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics. (English) Zbl 1098.76547 Physica D 170, No. 3-4, 253-286 (2002). MSC: 76F06 PDFBibTeX XMLCite \textit{D. D. Holm}, Physica D 170, No. 3--4, 253--286 (2002; Zbl 1098.76547) Full Text: DOI arXiv
Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. The Navier-Stokes-alpha model of fluid turbulence. (English) Zbl 1037.76022 Physica D 152-153, 505-519 (2001). MSC: 76F02 76D05 76F65 PDFBibTeX XMLCite \textit{C. Foias} et al., Physica D 152--153, 505--519 (2001; Zbl 1037.76022) Full Text: DOI arXiv
Cendra, Hernán; Holm, Darryl D.; Hoyle, Mark J. W.; Marsden, Jerrold E. The Maxwell-Vlasov equations in Euler-Poincaré form. (English) Zbl 1031.76555 J. Math. Phys. 39, No. 6, 3138-3157 (1998). MSC: 76X05 82D10 76M30 58Jxx PDFBibTeX XMLCite \textit{H. Cendra} et al., J. Math. Phys. 39, No. 6, 3138--3157 (1998; Zbl 1031.76555) Full Text: DOI arXiv
Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. The Euler-Poincaré equations and semidirect products with applications to continuum theories. (English) Zbl 0951.37020 Adv. Math. 137, No. 1, 1-81 (1998). Reviewer: Samir Musayev (Baku) MSC: 37K05 37K30 37N10 PDFBibTeX XMLCite \textit{D. D. Holm} et al., Adv. Math. 137, No. 1, 1--81 (1998; Zbl 0951.37020) Full Text: DOI arXiv
Gjaja, Ivan; Holm, Darryl D. Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid. (English) Zbl 0900.76718 Physica D 98, No. 2-4, 343-378 (1996). MSC: 76U05 86A05 76V05 70H05 PDFBibTeX XMLCite \textit{I. Gjaja} and \textit{D. D. Holm}, Physica D 98, No. 2--4, 343--378 (1996; Zbl 0900.76718) Full Text: DOI
Camassa, Roberto; Holm, Darryl D.; Levermore, C. David Long-time effects of bottom topography in shallow water. (English) Zbl 0899.76081 Physica D 98, No. 2-4, 258-286 (1996). MSC: 76B15 76U05 86A05 37N99 PDFBibTeX XMLCite \textit{R. Camassa} et al., Physica D 98, No. 2--4, 258--286 (1996; Zbl 0899.76081) Full Text: DOI
Holm, Darryl D.; Kovačič, Gregor Homoclinic chaos in a laser-matter system. (English) Zbl 0757.35082 Physica D 56, No. 2-3, 270-300 (1992). MSC: 35Q60 78A60 37D45 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{G. Kovačič}, Physica D 56, No. 2--3, 270--300 (1992; Zbl 0757.35082) Full Text: DOI
Holm, Darryl D.; Kovačič, Gregor Homoclinic chaos for ray optics in a fiber. (English) Zbl 0756.58027 Physica D 51, No. 1-3, 177-188 (1991). Reviewer: S.I.Andersson (Göteborg) MSC: 37C75 78A60 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{G. Kovačič}, Physica D 51, No. 1--3, 177--188 (1991; Zbl 0756.58027) Full Text: DOI
David, D.; Holm, D. D.; Tratnik, M. V. Hamiltonian chaos in nonlinear optical polarization dynamics. (English) Zbl 1211.37097 Phys. Rep. 187, No. 6, 281-367 (1990). MSC: 37N20 37D45 78A60 PDFBibTeX XMLCite \textit{D. David} et al., Phys. Rep. 187, No. 6, 281--367 (1990; Zbl 1211.37097) Full Text: DOI
Holm, Darryl D. Hall magnetohydrodynamics: Conservation laws and Lyapunov stability. (English) Zbl 0627.76134 Phys. Fluids 30, 1310-1322 (1987). Reviewer: V.Čadež MSC: 76X05 76E25 76M99 PDFBibTeX XMLCite \textit{D. D. Holm}, Phys. Fluids 30, 1310--1322 (1987; Zbl 0627.76134) Full Text: DOI
Holm, Darryl D. Hamiltonian dynamics and stability analysis of neutral electromagnetic fluids with induction. (English) Zbl 0617.76051 Physica D 25, 261-287 (1987). Reviewer: K.Čadež MSC: 76E25 70H99 76Y05 83A05 22E70 37J99 83C40 PDFBibTeX XMLCite \textit{D. D. Holm}, Physica D 25, 261--287 (1987; Zbl 0617.76051) Full Text: DOI
Holm, Darryl D. Gyroscopic analog for collective motion of a stratified fluid. (English) Zbl 0633.76116 J. Math. Anal. Appl. 117, 57-80 (1986). MSC: 76V05 70E05 PDFBibTeX XMLCite \textit{D. D. Holm}, J. Math. Anal. Appl. 117, 57--80 (1986; Zbl 0633.76116) Full Text: DOI
Holm, Darryl D.; Kupershmidt, Boris A. Lyapunov stability of relativistic fluids and plasmas. (English) Zbl 0618.76044 Phys. Fluids 29, 49-68 (1986). Reviewer: C.Brans MSC: 76E30 70K20 76Y05 76T99 76X05 35B35 83C55 37C75 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{B. A. Kupershmidt}, Phys. Fluids 29, 49--68 (1986; Zbl 0618.76044) Full Text: DOI
Similon, Philippe L.; Kaufman, Allan N.; Holm, Darryl D. Oscillation center theory and ponderomotive stabilization of low- frequency plasma modes. (English) Zbl 0615.76056 Phys. Fluids 29, 1908-1922 (1986). Reviewer: R.J.Gribben MSC: 76E25 76X05 82D10 PDFBibTeX XMLCite \textit{P. L. Similon} et al., Phys. Fluids 29, 1908--1922 (1986; Zbl 0615.76056) Full Text: DOI Link
Holm, Darryl D.; Kupershmidt, Boris A. Hamiltonian structure and Lyapunov stability of a hyperbolic system of two-phase flow equations including surface tension. (English) Zbl 0592.76144 Phys. Fluids 29, 986-991 (1986). MSC: 76T99 76E99 70M20 82B05 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{B. A. Kupershmidt}, Phys. Fluids 29, 986--991 (1986; Zbl 0592.76144) Full Text: DOI
Holm, Darryl D.; Kupershmidt, Boris A. Lyapunov stability conditions for relativistic multifluid plasma. (English) Zbl 0588.76205 Physica D 18, 405-409 (1986). MSC: 76Y05 76X05 70H05 83C55 70K20 76T99 76E25 PDFBibTeX XMLCite \textit{D. D. Holm} and \textit{B. A. Kupershmidt}, Physica D 18, 405--409 (1986; Zbl 0588.76205) Full Text: DOI
Holm, D. D.; Marsden, J. E.; Ratiu, T.; Weinstein, A. Nonlinear stability of fluid and plasma equilibria. (English) Zbl 0717.76051 Phys. Rep. 123, No. 1-2, 1-116 (1985). MSC: 76E30 76E25 76A02 PDFBibTeX XMLCite \textit{D. D. Holm} et al., Phys. Rep. 123, No. 1--2, 1--116 (1985; Zbl 0717.76051) Full Text: DOI Link
Holm, Darryl D. Magnetic tornadoes: Three-dimensional affine motions in ideal magnetohydrodynamics. (English) Zbl 0541.76058 Physica D 8, 170-182 (1983). MSC: 76E20 76W05 PDFBibTeX XMLCite \textit{D. D. Holm}, Physica D 8, 170--182 (1983; Zbl 0541.76058) Full Text: DOI