The Symmetric Regularized-Long-Wave Equation: Ill-posedness and Long Period Limit

摘要: In the present work we obtain two important results for Symmetric Regulraized-Long-Wave equation. First prove that initial value problem this equation is ill-posed data in $H^s(\mathbb{R})\times H^{s-1}(\mathbb{R}),$ if $s< 0,$ sense flow-map cannot be continuous at origin from H^{s-1}(\mathbb{R})$ to even $(\mathcal{D}'(\mathbb{R}))^2.$ We also establish an exact theory of convergence periodic solutions one, Sobolev spaces, as period goes infinity.