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Hall arising in modeling of river braiding: $$u_{yyt} - \\gamma u_{xxx} -\\alpha u_{yyyy} - \\beta u_{yy} + \\left (u^2 \\right)_{xyy} = 0$$ for $(x,y) \\in [0, 2\\pi] \\times [0, \\pi]$, $t> 0$, with boundary condition $u_{y}=0=u_{yyy}$ at $y=0$ and $y=\\pi$ and $2\\pi$ periodicity in $x$, using a contraction mapping argument in a Bourgain-type space $T_{s,b}$. 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