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Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients

In: Modern Stochastics and Applications

Author

Listed:
  • Shizan Fang

    (I.M.B, Université de Bourgogne)

Abstract

In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.

Suggested Citation

  • Shizan Fang, 2014. "Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 109-121, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-03512-3_7
    DOI: 10.1007/978-3-319-03512-3_7
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