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Type: Artigo de periódico
Title: Some results about a bidimensional version of the generalized BO
Author: Milanes, A
Abstract: For the bidimensional version of the generalized Benjamin-Ono equation: u(t) - H-(x) u(xy) + u(p)u(y) = 0, t is an element of R, (x, y) is an element of R-2, we use the method of parabolic regularization to prove local well-posedness in the spaces H-s (R-2), s > 2 and in the weighted spaces F-r(s) = H-s (R-2) boolean AND L-2 ((1 + x(2) + y(2))(r) dxdy), s > 2, r is an element of [0, 1] and F-1,k(k) = H-k (R-2) boolean AND L-2 ((1 + x(2) + y(2k))dxdy), k is an element of N, k greater than or equal to 3. As in the case of BO there is lack of persistence for both the linear and nonlinear equations (for p odd) in F-2(s). That leads to unique continuation principles in a natural way. By standard methods based on L-p - L-q estimates of the associated group we obtain global well-posedness for small initial data and nonlinear scattering for p greater than or equal to 3, s > 3. Nonexistence of square integrable solitary waves of the form u(x, y, t) = v(x, y - ct), c > 0, p is an element of {1, 2} is obtained using the results about existence of solitary waves of the BO and variational methods.
Subject: Benjamin-Ono equation
nonlinear dispersive equations
unique continuation principles
nonlinear scattering
solitary waves
Country: EUA
Editor: Amer Inst Mathematical Sciences
Citation: Communications On Pure And Applied Analysis. Amer Inst Mathematical Sciences, v. 2, n. 2, n. 233, n. 250, 2003.
Rights: aberto
Date Issue: 2003
Appears in Collections:Unicamp - Artigos e Outros Documentos

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