Positive solutions with prescribed mass for a planar Choquard equation with critical growth

We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of a positive radial solution by a variational argument, which exploits a delicate analysis on the mountain pass level. Under an additional monotonicity assumption on the nonlinearity, such a solution turns out to be also a ground state in H1(R2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>1(\mathbb {R}<^>2)$$\end{document}. Our work extends the results by Dou et al. (J Geom Anal 34(10):317, 2024) to the Choquard setting, improving in several directions those by Deng and Yu (Z Angew Math Phys 74(3):103, 2023).