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math.AP2023
Remarks on the Complex Euler Equations
Dallas Albritton, W. Jacob Ogden
We consider a complexification of the Euler equations introduced by Šverák which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analy…
math.AP2023
Linear and nonlinear instability of vortex columns
Dallas Albritton, Wojciech Ożański
We consider vortex column solutions to the D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes d…
math.AP2023
Sharp bounds on enstrophy growth for viscous scalar conservation laws
Dallas Albritton, Nicola De Nitti
We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admiss…