# American Institute of Mathematical Sciences

April  2011, 30(1): 253-259. doi: 10.3934/dcds.2011.30.253

## On the ill-posedness result for the BBM equation

 1 Centro de Matemática, Universidade do Minho, 4710-057, Braga, Portugal

Received  February 2010 Revised  September 2010 Published  February 2011

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in $H^s(\R)$, $s<0$ in the sense that the flow-map $u_0\mapsto u(t)$ that associates to initial data $u_0$ the solution $u$ cannot be continuous at the origin from $H^s(\R)$ to even $\mathcal{D}'(\R)$ at any fixed $t>0$ small enough. This result is sharp.
Citation: Mahendra Panthee. On the ill-posedness result for the BBM equation. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 253-259. doi: 10.3934/dcds.2011.30.253
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##### References:
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