Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces

Gerard Misiołek, Tsuyoshi Yoneda

We construct an example showing that the solution map of the Euler equations is not continuous in the Hölder space from $C^{1,\alpha }$ to $L_t^{\infty }{C}_x^{1,\alpha }$ for any $0<\alpha <1$. On the o…