LAUSR

Abstract The Cauchy problem of the fifth order Kadomtsev–Petviashvili-I equation (fifth-KP-I) (0.1) ∂ t u + ∂ x 5 u ± ∂ x 3 u − ∂ x − 1 ∂ y y u + ∂ x ( u 2 ) = 0 , ( x , y , t ) ∈ R 3 ; is considered. It follows that the fifth order Kadomtsev–Petviashvili-I equation (0.1) is locally well-posed in H s , 0 with s ≥ − 3 / 4 , where the norm H s , r is defined by ‖ f ‖ H ( x , y ) s , r = ‖ 〈 ξ 〉 s 〈 ζ 〉 r f ˆ ‖ L ( ξ , ζ ) 2 .