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math.AP2025
Non-uniqueness of mild solutions to supercritical heat equations
Irfan Glogić, Martina Hofmanová, Theresa Lange +1
We consider the focusing power nonlinearity heat equation \begin{equation}\label{Eq:Heat_abstract}\tag{NLH} \partial_t u -Δu = |u|^{p-1}u, \quad p>1, \end{equation} in dimensions $…
math.AP2024
Non-uniqueness of Leray--Hopf solutions for the fractional Navier--Stokes equations perturbed by transport noise
Theresa Lange, Marco Rehmeier, Andre Schenke
For the fractional Navier--Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically stro…