Microglobal analysis of the Euler equations

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue 3 SUPPL., 2005, Pages

  Shnirelman, Alexander ^a  

^a Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Fredholm maps; Group of diffeomorphisms; Ideal incompressible fluid; Paradifferential operators

Indexed keywords

GEODESY; INCOMPRESSIBLE FLOW; VECTORS; VELOCITY MEASUREMENT;

FREDHOLM MAPS; GROUP OF DIFFEOMORPHISMS; IDEAL INCOMPRESSIBLE FLUIDS; PARADIFFERENTIAL OPERATORS;

EQUATIONS OF MOTION;

EULER FLOW; FLUID DYNAMICS; INCOMPRESSIBLE FLUID;

EID: 23944431624     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-005-0167-5     Document Type: Article

References (16)

1. [A] S. ALINHAC, Paracomposition et operateurs paradifferentielles, Oomm. Partial Differential Equations 11 (1986), 87-121.
2. [AK] V. ARNOLD and B. KHESIN, Topological Methods in Hydrodynamics, Springer, New York, 1998.
3. [B] J.-M. BONY, Calcul symbolique et propagation des singularités pour les equations aux derivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4) 14 (1981), 209-246.
4. [EM] D. G. EBIN and J. MARSDEN, Groups of diffeomorphisms and the motion of an ideal incompressible fluid, Ann. of Math. 92 (1970), 102-163.
5. [BMP] D. G. EBIN, G. MISIOLEK and S. P. PRESTON, Singularities of the exponential map on the volume-preserving diffeomorphism group, Preprint, 2005, 18 p.
6. [G] N. M. GUNTER, On the motion of a fluid contained in a given moving vessel (in Russian), Izvestia AN USSR, Sect. Phys. Math. (1926), 1323-1328; 1503-1532;
7. N. M. GUNTER, On the motion of a fluid contained in a given moving vessel (in Russian), Izvestia AN USSR, Sect. Phys. Math. (1927), 621-656
8. 1139-1162; N. M. GUNTER, On the motion of a fluid contained in a given moving vessel (in Russian), Izvestia AN USSR, Sect. Phys. Math. (1928), 9-30.
9. [L] L. LICHTENSTEIN, Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosiger Flüssigkeiten und die Helmholtzischen Wirbelsätze, Math. Z. 23 (1925), 89-154, 309-316;
10. L. LICHTENSTEIN, Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosiger Flüssigkeiten und die Helmholtzischen Wirbelsätze, Math. Z. 26 (1927), 196-323;
11. L. LICHTENSTEIN, Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosiger Flüssigkeiten und die Helmholtzischen Wirbelsätze, Math. Z. 28 (1928), 387-415, 725;
12. L. LICHTENSTEIN, Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosiger Flüssigkeiten und die Helmholtzischen Wirbelsätze, Math. Z. 32 (1930), 608.
13. 2), Proc. Amer. Math. Soc. 124 (1996).
14. [S1] A. SHNIRELMAN, The degree of the quasi-ruled mapping and the non-linear Hilbert problem (in Russian), Matematicheskij Sbornik 89 (3) (1972), 366-389.
15. English Transl. Mat. Sbornik 89 (3) (131) (1972), 373-396.
16. [S2] A. SHNIRELMAN, Evolution of singularities, generalized Liapunov function and generalized integral for an ideal incompressible fluid, Amer. J. Math. 119 (1997), 579-608.