Volume 8, Number 3, 2018, Pages 890914 DOI：10.11948/2018.890 
Wellposedness for the coupled BBM systems 
Hongqiu Chen and Cristina A. Haidau 
Keywords:Regularized long wave, coupled BBMBBM equations, nonlinear dispersive wave equations. 
Abstract: 
Consideration is given to initial value problem for systems of two evolution equations of generalized BBMtype coupled through nonlinearity described in (1.3). It is shown that the problem is always locally wellposed in the $L_2$based Sobolev spaces $H^s(\mathbb{R}) \times H^s(\mathbb{R})$ for $s \ge 0$. Under exact conditions on $A, \cdots, F,$ the local wellposedness theory extends globally, and bounds for the growth in time of relevant norms of solutions corresponding to very general auxiliary data are derived. 
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