Non-unique stationary solutions of forced SQG

We show the existence of non-unique stationary weak solutions for forced surface quasi-geostrophic (SQG) equation via a convex integration scheme. The scheme is implemented for the sum-difference system of two distinct solutions. Through this scheme, one observes the external forcing is naturally generated accompanying the flexibility in means of lack of unique-ness. It thus provides a transparent way to reveal the flexibility of the system with the presence of a forcing.