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math.AP2022
Hyperbolic -model on the plane
Tadahiro Oh, Leonardo Tolomeo, Yuzhao Wang +1
We study the hyperbolic -model on the plane. By establishing coming down from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we firs…
math.AP2022
Norm inflation for the derivative nonlinear Schrödinger equation
Yuzhao Wang, Younes Zine
In this note, we study the ill-posedness problem for the derivative nonlinear Schrödinger equation (DNLS) in the one-dimensional setting. More precisely, by using a ternary-quinary…
math.AP2022
Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity
Ilya Chevyrev, Tadahiro Oh, Yuzhao Wang
We consider the ill-posedness issue for the cubic nonlinear heat equation and prove norm inflation with infinite loss of regularity in the Hölder-Besov space $\mathcal C^s = B^{s}_…