3 papers
math.AP2026
Hadamard ill-Posedness of the linearised Prandtl Equations in Gevrey spaces
Francesco De Anna, Joshua Kortum
We prove Hadamard ill-posedness for the non-autonomous linearised Prandtl equations around time-dependent shear-flow equilibria in function spaces up to Gevrey class 4. More precis…
math.AP2025
Linear Instability of the Prandtl Equations via Hypergeometric Functions and the Harmonic Oscillator
Francesco De Anna, Joshua Kortum
We establish a deep connection between the Prandtl equations linearised around a quadratic shear flow, confluent hypergeometric functions of the first kind, and the Schrödinger op…
math.AP2024
Existence and compactness of global weak solutions of three-dimensional axisymmetric Ericksen-Leslie system
Joshua Kortum, Changyou Wang
In dimension three, the existence of global weak solutions to the axisymmetric simplified Ericksen-Leslie system without swirl is established. This is achieved by analyzing weak co…