Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

• Published in: Stochastic partial differential equations : analysis and computations Vol. 9; no. 2; pp. 491 - 509
• Main Authors: Da Prato, Giuseppe, Flandoli, Franco, Röckner, Michael
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-06-2021; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Continuity equation; Euler-Lagrange equation; Eulers equations; Hilbert space; Mathematical analysis; Mathematics; Mathematics and Statistics; Numerical Analysis; Partial Differential Equations; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Random initial conditions; Euler equations; Continuity equation; Enstrophy measure
• ISSN: 2194-0401; 2194-041X
• DOI: 10.1007/s40072-020-00173-8

The 2D Euler equations with random initial condition has been investigates by Albeverio and Cruzeiro (Commun Math Phys 129:431–444,
1990
) and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure.