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| We consider two-dimensional fluid models, such as the Euler equations, the surface quasi-geostrophic equations, the incompressible porous media equation, and the Boussinesq equations. We prove that as long as the velocity field stays $C^{1,\alpha}$ for some $\alpha \in (0,1)$, the Lagrangian particle trajectories are real-analytic functions of time. |
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