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4 - Lecture notes on variational models for incompressible Euler equations

from PART 1 - SHORT COURSES

Published online by Cambridge University Press:  05 August 2014

By
Luigi Ambrosio  and
Alessio Figalli
Edited by
Yann Ollivier ,
Hervé Pajot  and
Cedric Villani
Luigi Ambrosio
Affiliation:
Italy
Alessio Figalli
Affiliation:
University of Texas
Yann Ollivier
Affiliation:
Université de Paris XI
Hervé Pajot
Affiliation:
Université de Grenoble
Cedric Villani
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
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Type
Chapter
Information
Optimal Transport
Theory and Applications
 , pp. 58 - 71
Publisher: Cambridge University Press
Print publication year: 2014

References

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[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.Google Scholar
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[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.Google Scholar
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[10] D.G., Ebin and J., Marsden, Groups of diffeomorphisms and the motion of an ideal incompressible fluid, Ann. Math., 2 (1970), 102–163.Google Scholar
[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.Google Scholar
[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).Google Scholar
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[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.Google Scholar
[16] V., Yudovich, Some bounds for solutions of elliptic equations, Am. Math. Soc. Transl. (2) 56 (1962).Google Scholar

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