Infinitely many smooth nonradial finite-energy stationary SQG solutions are claimed, built from sign-changing k-bubble solutions of (−Δ)^{1/2}ψ = ψ³ concentrated at polygon vertices at scale (k log k)^{−2}.
Non-unique stationary solutions of forced SQG
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abstract
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.
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Smooth nonradial stationary solutions to SQG via the half-Yamabe equation
Infinitely many smooth nonradial finite-energy stationary SQG solutions are claimed, built from sign-changing k-bubble solutions of (−Δ)^{1/2}ψ = ψ³ concentrated at polygon vertices at scale (k log k)^{−2}.