Skip to main content Accessibility help
×
Home
  • Access
  • Print publication year: 2014
  • Online publication date: August 2014

4 - Lecture notes on variational models for incompressible Euler equations

from PART 1 - SHORT COURSES
    • Send chapter to Kindle

      To send this chapter to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Available formats
      ×

      Send chapter to Dropbox

      To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

      Available formats
      ×

      Send chapter to Google Drive

      To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

      Available formats
      ×
[1] L., Ambrosio and A., Figalli, Geodesies in the space of measure-preserving maps and plans, Arch. Ration. Math. Anal., 194 (2009), no. 2, 421–462.
[2] L., Ambrosio and A., Figalli, On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations, Calc. Var. Partial Dif. Equations, 31 (2008), 497–509.
[3] V., Arnold, Sur la geometrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble), 16 (1966), fase. 1, 319-361.
[4] M., Bernot, A., Figalli and F., Santambrogio, Generalized solutions for the Euler equations in one and two dimensions, J. Math. Pures Appl., 91 (2008), no. 2, 137-155.
[5] Y., Brenier, The least action principle and the related concept of generalized flows for incompressible perfect fluids, J. Am. Math. Soc., 2 (1989), 225–255.
[6] Y., Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Commun. Pure Appl. Math., 44 (1991), 375–417.
[7] Y., Brenier, The dual least action problem for an ideal, incompressible fluid, Arch. Rational Mech. Anal., 122 (1993), 323–351.
[8] Y., Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Commun. Pure Appl. Math., 52 (1999), 411–452.
[9] Y., Brenier and W., Gangbo, Lp approximation of maps by diffeomorphisms, Calc. Var. Partial Dif. Equations, 16 (2003), no. 2, 147–164.
[10] D.G., Ebin and J., Marsden, Groups of diffeomorphisms and the motion of an ideal incompressible fluid, Ann. Math., 2 (1970), 102–163.
[11] A., Figalli and V., MandorinoFine properties of minimizers of mechanical Lagrangians with Sobolev potentials, Discrete Contin. Dyn. Syst., 31 (2011), no. 4, 1325–1346.
[12] A.I., Shnirelman, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sb. (N.S.), 128 (170) (1985), no. 1, 82-109 (in Russian).
[13] A.I., Shnirelman, Generalized fluid flows, their approximation and applications, Geom. Funct. Anal., 4 (1994), no. 5, 586–620.
[14] C., Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, vol. 58, American Mathematical Society, Providence, RI, 2003.
[15] V., Yudovich, Nonstationary flow of an ideal incompressible liquid, Zhurn. Vych. Mat., 3 (1963), 1032–1066.
[16] V., Yudovich, Some bounds for solutions of elliptic equations, Am. Math. Soc. Transl. (2) 56 (1962).