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# Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models

## Author(s): Constantin, Peter; Vicol, Vlad C.; Wu, Jiahong

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 Abstract: We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at least for short time. We show that they have real analytic Lagrangian paths. More precisely, we show that as long as a solution of any of these equations is in a class of regularity that assures Hölder continuous gradients of velocity, the corresponding Lagrangian paths are real analytic functions of time. The method of proof is conceptually straightforward and general, and we address the combinatorial issues head-on. Publication Date: 5-Nov-2015 Electronic Publication Date: 28-Aug-2015 Citation: Constantin, Peter, Vicol, Vlad, Wu, Jiahong. (2015). Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models. ADVANCES IN MATHEMATICS, 285 (352 - 393. doi:10.1016/j.aim.2015.05.019 DOI: doi:10.1016/j.aim.2015.05.019 ISSN: 0001-8708 EISSN: 1090-2082 Pages: 352 - 393 Type of Material: Journal Article Journal/Proceeding Title: ADVANCES IN MATHEMATICS Version: Author's manuscript

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