Convex integration has for a decade now been used to produce impressive examples of the flexibility of weak solutions to fluid equations. Still, for many models there remains a gap between the regularity of the construction and the known or conjectured regularity at which uniqueness holds for the Cauchy problem. In this talk we present a new alternating approach to convex integration for forced models. As a consequence one obtains non-uniqueness results for forced 2D Euler, 3D Euler, and SQG, in some cases with higher regularity than possible with previous convex integration schemes.

This is joint work with Aynur Bulut and Manh Khang Huynh.