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تسجيل مستخدم جديدA remark on ill-posedness
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Norm inflation implies certain discontinuous dependence of the solution on the initial value. The well-posedness of the mild solution means the existence and uniqueness of the fixed points of the corresponding integral equation. For ${rm BMO}^{-1}$, Auscher-Dubois-Tchamitchian proved that Koch-Tatarus solution is stable. In this paper, we construct a non-Gauss flow function to show that, for classic Navier-Stokes equations, wellposedness and norm inflation may have no conflict and stability may have meaning different to $L^{infty}(({rm BMO}^{-1})^{n})$.
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