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Sharp global well‐posedness for the fractional BBM equation
Author(s) -
Wang Ming,
Zhang Zaiyun
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5109
Subject(s) - mathematics , bilinear interpolation , initial value problem , mathematical analysis , cauchy problem , contraction (grammar) , contraction mapping , exponent , real line , fixed point theorem , medicine , linguistics , statistics , philosophy
The Cauchy problem of the fractional Benjamin‐Bona‐Mahony equation with exponent α ∈ (1,2] on the real line is studied. First, some bilinear estimates for the fractional Benjamin‐Bona‐Mahony are proved, and the estimates are shown to be sharp by providing counter‐examples. Second, the local well‐posedness in H s with s ≥ max { 0 , 3 2 − α } is proved by the contraction principle. Finally, the local solution is extended to a global one by the I ‐method. The well‐posedness result turns out to be sharp and fills the gap between the results in Discrete Contin. Dyn. Syst, 23 (2009) 1253‐1275 and that in Discrete Contin. Dyn. Syst., 30 (2011) 253‐259.