7 papers · 1 filter
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…
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 ope…
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…
Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations
Francesco De Anna, Joshua Kortum, Stefano Scrobogna
We address a physically-meaningful extension of the Prandtl system, also known as hyperbolic Prandtl equations. We show that the linearised model around a non-monotonic shear flow…
Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids
Francesco De Anna, Joshua Kortum, Anja Schlömerkemper
In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids…
Concentration-cancellation in the Ericksen-Leslie model
Joshua Kortum
We establish the subconvergence of weak solutions to the Ginzburg-Landau approximation to global-in-time weak solutions of the Ericksen-Leslie model for nematic liquid crystals on…