Ill-posedness of Basic Equations of Fluid Dynamics in Besov Spaces
نویسنده
چکیده
We give a construction of a divergence-free vector field u0 ∈ H s ∩ B ∞,∞ , for all s < 1/2, such that any Leray-Hopf solution to the Navier-Stokes equation starting from u0 is discontinuous at t = 0 in the metric of B ∞,∞ . For the Euler equation a similar result is proved in all Besov spaces B r,∞ where s > 0 if r > 2, and s > n(2/r − 1) if 1 ≤ r ≤ 2.
منابع مشابه
Persistence of the incompressible Euler equations in a Besov space B d + , ( R d )
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تاریخ انتشار 2009