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On global well-posedness for a class of nonlocal dispersive wave equations. (English) Zbl 1117.35071
The authors deal with the initial value problem for the following class of one-dimensional nonlocal dispersive wave equations $u_t+ D^{1+\alpha}_x\partial_x u+ uu_x= 0,\quad u(0)= u_0,\tag{1}$ where $$D^{1+\alpha}_x$$ denotes the Fourier multiplier with symbols $$|\xi|^{1+\alpha}$$, $$0\leq\alpha\leq 1$$. The authors prove global well-posedness for (1) in Sobolev spaces with weighted low frequencies.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35R10 Functional partial differential equations
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