On well/illposedness for generalized SQG equations with singular velocities (1)

Speaker: In-Jee Jeong 教授  韩国高等研究院（KIAS）

Inviter:  秦国林 博士

Title: On well/illposedness for generalized SQG equations with singular velocities (1)

Language: English

Time & Venue: 2026.03.20 9:00-10:00  南楼202

Abstract: We prove strong illposedness for the generalized SQG equations for smooth data, when the stream function is more singular than the advected scalar. The illposedness mechanism is due to degenerate dispersion near a quadratic shear flow. In the course of the proof, we develop a robust method for the construction of degenerating wave packets, which should be useful for more complicated systems. Such "singular SQG" equations appear in physics, including the so-called asymptotic model in LQG (large-scale quasi-geostrophic) and the electron-MHD model. The case when the stream function is logarithmically singular is of particular interest ("Ohkitani model"); in this case, there is wellposedness in a scale of Sobolev spaces with time-decreasing exponents, with applications to long-time dynamics of inviscid and viscous alpha-SQG models. Joint work with D. Chae, Jungkyoung Na and S.-J. Oh.