
## 1. Global solutions to SQG equation

The Surface Quasi-Geostrophic (SQG) equation is a simple 2D model, whose dynamics still nead to be understood.
1. ### Existence of global weak solutions

#### Problem 1.1.

[Andrea Nahmod] The modified SQG (mSQG) equation reads \begin{aligned} \partial_t\theta +u\cdot \nabla\theta &=0, \\ u &= \mathcal{R}^\perp|\nabla|^{-\varepsilon}\theta, \end{aligned} where $\theta : \mathbb{R}\times\mathbb{R}^2\to\mathbb{R}$, $\varepsilon>0$, and $\mathcal{R}$ is the Riesz transform. Is it possible to find global weak solutions to (mSQG) when $\varepsilon=0$, with respect to random initial data ?
• ### Towards strong global solutions ?

#### Problem 1.2.

[Alex Ionescu] Is it possible to describe the formation of singularities in (mSQG) ?