| Abstract: |
| In a given phase space, it is very interesting to find out the critical exponent of growth order for the nonlinear term, such that the nonlinear system has a global attractor. However, the problem does not exists for the Benjamin-Bona-Mahony (BBM) equation, since the nonlinear term is given by $uu_x$. In this case, an ``equivalent`` question is to find out the lowest regularity space in which the global attractor exists. In this talk, we shall give some results for the global attractor for the BBM equations in low regularity spaces with low regularity forces. |
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