On global well-posedness for a class of nonlocal dispersive wave equations (Q874713)

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.