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Global well-posedness of the periodic Majda-Biello systems in the resonant case
We study the Cauchy problem for the following Majda-Biello system in the resonant case $α\in (0,4]\setminus\{1\}$ on the periodic domain $\mathbb{T}$. \[ \left\{ \begin{array}{rcl} u_{t} + u_{xxx} & = & - v v_x, v_{t} + αv_{xxx} & = & - (uv)_{x}, (u,v)|_{t=0} & = & (u_0,v_0), \end{array} \righ
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