  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 uniqueness. It thus provides a
transparent way to reveal the flexibility of the system with the presence of a
forcing.

Analysis of PDEs