On the search for singularities in incompressible flows

Diego Córdoba

Applications of Mathematics (2006)

  • Volume: 51, Issue: 4, page 299-320
  • ISSN: 0862-7940

Abstract

top
In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.

How to cite

top

Córdoba, Diego. "On the search for singularities in incompressible flows." Applications of Mathematics 51.4 (2006): 299-320. <http://eudml.org/doc/33257>.

@article{Córdoba2006,
abstract = {In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.},
author = {Córdoba, Diego},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; singularities; incompressible flows; Navier-Stokes equations; singularities; incompressible flows},
language = {eng},
number = {4},
pages = {299-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the search for singularities in incompressible flows},
url = {http://eudml.org/doc/33257},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Córdoba, Diego
TI - On the search for singularities in incompressible flows
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 299
EP - 320
AB - In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.
LA - eng
KW - Navier-Stokes equations; singularities; incompressible flows; Navier-Stokes equations; singularities; incompressible flows
UR - http://eudml.org/doc/33257
ER -

References

top
  1. 10.1007/BF01212349, Commun. Math. Phys. 94 (1984), 61–66. (1984) MR0763762DOI10.1007/BF01212349
  2. 10.1007/BF02097055, Commun. Math. Phys. 152 (1993), 19–28. (1993) MR1207667DOI10.1007/BF02097055
  3. Vorticity and the Mathematical Theory of Incompresible Fluid Flow. Cambridge Texts in Applied Mathematics No.  27, Cambridge University Press, Cambridge, 2002. (2002) MR1867882
  4. 10.1007/s00205-003-0271-8, Arch. Ration. Mech. Anal. 170 (2003), 185–210. (2003) Zbl1093.76005MR2020259DOI10.1007/s00205-003-0271-8
  5. 10.1088/0951-7715/16/2/307, Nonlinearity 16 (2003), 479–495. (2003) Zbl1029.35006MR1958612DOI10.1088/0951-7715/16/2/307
  6. 10.1007/s00220-002-0750-z, Commun. Math. Phys. 233 (2003), 297–311. (2003) MR1962043DOI10.1007/s00220-002-0750-z
  7. 10.24033/asens.1679, Ann. Sci. Ec. Norm. Supér. 26 (1993), 517–542. (French) (1993) Zbl0779.76011MR1235440DOI10.24033/asens.1679
  8. 10.1103/PhysRevLett.89.184501, Phys. Rev. Lett. 89 (2002), 1804501–1804504. (2002) DOI10.1103/PhysRevLett.89.184501
  9. 10.1512/iumj.2001.50.2153, Indiana Univ. Math. J. 50 (2001), 97–107. (2001) MR1855665DOI10.1512/iumj.2001.50.2153
  10. 10.1080/03605309608821197, Commun. Partial Differ. Equation 21 (1996), 559–571. (1996) MR1387460DOI10.1080/03605309608821197
  11. 10.1088/0951-7715/7/6/001, Nonlinearity 7 (1994), 1495–1533. (1994) MR1304437DOI10.1088/0951-7715/7/6/001
  12. 10.1016/S0375-9601(98)00108-X, Phys. Lett.  A 241 (1998), 168–172. (1998) MR1613907DOI10.1016/S0375-9601(98)00108-X
  13. 10.1137/S0036141098337333, SIAM J.  Math. Anal. 30 (1999), 937–948. (1999) Zbl0957.76093MR1709781DOI10.1137/S0036141098337333
  14. 10.1073/pnas.2036515100, Proc. Natl. Acad. Sci. USA 100 (2003), 15316–15317. (2003) MR2032097DOI10.1073/pnas.2036515100
  15. 10.1007/s00220-004-1055-1, Commun. Math. Phys. 249 (2004), 511–528. (2004) MR2084005DOI10.1007/s00220-004-1055-1
  16. 10.1016/j.aim.2003.08.009, Adv. Math. 187 (2004), 228–239. (2004) MR2074177DOI10.1016/j.aim.2003.08.009
  17. 10.2307/121037, Ann. Math. 148 (1998), 1135–1152. (1998) MR1670077DOI10.2307/121037
  18. 10.1007/s002200100502, Commun. Math. Phys. 222 (2001), 293–298. (2001) MR1859600DOI10.1007/s002200100502
  19. 10.1137/S0036141003424095, SIAM J.  Math. Anal. 36 (2004), 204–213. (2004) MR2083858DOI10.1137/S0036141003424095
  20. 10.1073/pnas.0308154101, Proc. Natl. Acad. Sci. USA 101 (2004), 2687–2691. (2004) MR2036970DOI10.1073/pnas.0308154101
  21. 10.1073/pnas.0501977102, Proc. Natl. Acad. Sci. USA 102 (2005), 5949–5952. (2005) MR2141918DOI10.1073/pnas.0501977102
  22. 10.1007/BF01393835, Invent. Math. 98 (1989), 511–547. (1989) MR1022305DOI10.1007/BF01393835
  23. Applied analysis of the Navier Stokes equations, Cambridge University Press, Cambridge, 1995. (1995) MR1325465
  24. 10.1080/03605308108820180, Commun. Partial Differ. Equations 6 (1981), 329–359. (1981) MR0607552DOI10.1080/03605308108820180
  25. 10.1017/S0022112095000012, J.  Fluid Mech. 282 (1995), 1–20. (1995) MR1312238DOI10.1017/S0022112095000012
  26. 10.1007/s00220-004-1256-7, Commun. Math. Phys. 255 (2005), 161–181. (2005) Zbl1088.37049MR2123380DOI10.1007/s00220-004-1256-7
  27. 10.1007/s002200000267, Commun. Math. Phys. 214 (2000), 191–200. (2000) MR1794270DOI10.1007/s002200000267
  28. On the separation of droplets from a liquid jet, Fluid Dyn. Res. 17 (1996), 121–145. (1996) 
  29. 10.1063/1.869184, Phys. Fluids 9 (1997), 876–882. (1997) MR1437554DOI10.1063/1.869184
  30. Geophysical Fluid Dynamics, Springer-Verlag, New York, 1987. (1987) Zbl0713.76005
  31. Smithsonian Report 250, 1863. (1863) 
  32. On the instability of jets, Proc. L.  M.  S. 10 (1879), 4–13. (1879) 
  33. Dynamical problem in nonlinear advective partial differential equations, PhD.  Thesis, University of Chicago, 1995. (1995) 
  34. 10.1002/cpa.20059, Commun. Pure Appl. Math. 58 (2005), 821–866. (2005) Zbl1073.35006MR2142632DOI10.1002/cpa.20059
  35. Lectures on Geophysical Fluid Dynamics, Oxford University Press, New York, 1998. (1998) MR1718369
  36. Mémoire sur la Constitution des veines liquides lancées par des orifices circulaires en mince paroi, Ann. Chim. Phys. 53 (1833), 337–386. (French) (1833) 
  37. 10.1126/science.265.5169.219, Science 265 (1994), 219–222. (1994) MR1282463DOI10.1126/science.265.5169.219
  38. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. (1970) Zbl0207.13501MR0290095
  39. Harmonic Analysis, Princeton University Press, Princeton, 1993. (1993) Zbl0821.42001MR1232192
  40. 10.1017/S0022112097005570, J.  Fluid Mech. 341 (1997), 269–294. (1997) MR1457712DOI10.1017/S0022112097005570
  41. Topics in Nonlinear Analysis. Publications Mat. D’Orsay, No.  7813, Univ. de Paris-Sud, Orsay, 1978. (1978) MR0532371

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.