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arXiv · 2608.23059

Existence of weak solutions to the generalized SQG equations in Sobolev spaces

Anuj Kumar
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Abstract

We consider the two-dimensional dissipative generalized surface quasi-geostrophic equations given by \[\partial_t \theta+u\cdot \nabla \theta+\nu (-\Delta)^{\alpha}\theta=0,\quad u=\nabla^{\perp}\Lambda^{\beta-2}\theta\] and establish global existence of weak solutions with initial data in $\dot{H}^{\frac{\beta}{2}-1}(\mathbb{R}^2)$. Our result extends the framework of Marchand's solutions (Comm. Math. Phys. 277 (2008), no. 1, 45-67) to this larger family of active scalar equations.

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Anuj Kumar. 2026-08-24. Existence of weak solutions to the generalized SQG equations in Sobolev spaces. https://arxiv.org/abs/2608.23059

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