Local well-posedness for the Sixth-Order Boussinesq Equation

Details Local well-posedness for the Sixth-Order Boussinesq Equation Local well-posedness for the Sixth-Order Boussinesq Equation

2010-12-22

arxiv.org/abs/1012.5088v1

Journal of Mathematical Analysis and Applications, Volume 385, Issue 1, 1 January 2012, Pages 230-242

Mathematics

Analysis of PDEs

16 pages. Submitted

Scientific paper

This work studies the local well-posedness of the initial-value problem for
the nonlinear sixth-order Boussinesq equation $u_{tt}=u_{xx}+\beta
u_{xxxx}+u_{xxxxxx}+(u^2)_{xx}$, where $\beta=\pm1$. We prove local
well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\R)$
for negative indices of $s \in \R$.

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