We prove a result on the existence and uniqueness of a local solution to a generalized Boussinesq equation for initial data of low regularity. We also discuss the existence of global solutions and the occurrence of blow-up phenomena. Our results are applicable to several physically relevant equations that are obtained as special cases of our model equation.
"The initial value problem for a generalized Boussinesq equation." Differential Integral Equations 15 (9) 1061 - 1072, 2002.