| Abstract: |
| We consider the coupled KPZ equation on a one-dimensional unit interval with periodic boundary condition. This equation is ill-posed in a usual sense. We discuss the local well-posedness, convergence of solutions of two types of approximating equations, invariant measures and global well-posedness under the trilinear condition (T) for the coupling constant, the role of the condition (T) in view of invariant measures and renormalizations for 4th order terms, an example which does not satisfy (T) but has an invariant measure, and the cross-diffusion case. |
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