On the Cauchy problem for dispersive equations with nonlinear terms involving high derivatives and with arbitrarily large initial data
نویسنده
چکیده
iut + Lu = F (u), (1) where u : IR × IR → I C and L is a linear (pseudo -) differential operator of order m with real valued symbol denoted by l(ξ), and F is a nonlinear, possibly nonlocal operator. We will only consider the case where the linear part of (1) is dispersive, i.e. l(ξ) 6= Cξ. Actually, we will address cases where the linear group e satisfies some “decay” properties, see Section 1.2 below. The nonlinear term in (1) will be of the following form :
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