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WELL-POSEDNESS FOR A HIGHER-ORDER BENJAMIN-ONO FELIPE LINARES, DIDIER PILOD, AND GUSTAVO PONCE
 

Summary: WELL-POSEDNESS FOR A HIGHER-ORDER BENJAMIN-ONO
EQUATION
FELIPE LINARES, DIDIER PILOD, AND GUSTAVO PONCE
Abstract. In this paper we prove that the initial value problem associated
to the following higher-order Benjamin-Ono equation
tv - bH2
xv + a3
xv = cvxv - dx(vHxv + H(vxv)),
where x, t R, v is a real-valued function, H is the Hilbert transform, a R,
b, c and d are positive constants, is locally well-posed for initial data
v(0) = v0 Hs
(R), s 2 or v0 Hk
(R) L2
(R; x2
dx), k Z+, k 2.
1. Introduction
We study the initial value problem (IVP) associated to the following higher-order
Benjamin-Ono equation
(1.1)
tv - bH2

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics