The global solution and blow-up phenomena to a modified Novikov equation

A modified Novikov equation with symmetric coefficients is investigated. Provided that the initial value u 0 ∈ H s ( R ) ( s > 3 2 ), ( 1 − ∂ x 2 ) u 0 does not change sign and the solution u itself belongs to L 1 ( R ) , the existence and uniqueness of the global strong solutions to the equation are established in the space C ( [ 0 , ∞ ) ; H s ( R ) ) ∩ C 1 ( [ 0 , ∞ ) ; H s − 1 ( R ) ) . A blow-up result to the development of singularities in finite time for the equation is acquired.