I will discuss two recent works on the limits of analytic smoothing in dissipative fluid models. The first establishes lower bounds for Fourier tails in the cheap Navier–Stokes model, describing their persistence and generation and giving upper bounds for the analyticity radius. The second constructs fluid models showing that exact quadratic energy cancellation alone does not force this radius to grow, including a projected dissipative surface quasi-geostrophic model in which entire analyticity is lost. Together, these results clarify how nonlinear interactions constrain analytic regularization.

The talk is based on joint works with Weixi Li and Ping Zhang, and with Ke Chen, Haina Li, and Ping Zhang, respectively.