On the Local Regularity of the Kp-i Equation in Anisotropic Sobolev Space
نویسندگان
چکیده
We prove that the KP-I initial-value problem { ∂tu+ ∂ 3 xu− ∂ x ∂ yu+ ∂x(u/2) = 0 on Rx,y × Rt; u(x, y, 0) = φ(x, y), is locally well-posed in the space H(R) = {φ ∈ L(R) : ‖φ‖H1,0(R2) ≈ ‖φ‖L2 + ‖∂xφ‖L2 < ∞}.
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