# Almost sure global well-posedness for the energy supercritical Schr\"odinger equations.

@article{Sy2020AlmostSG, title={Almost sure global well-posedness for the energy supercritical Schr\"odinger equations.}, author={Mouhamadou Sy}, journal={arXiv: Analysis of PDEs}, year={2020} }

We consider the Schr\"odinger equation with any power non-linearity on the three-dimensional torus. We construct non-trivial measures supported on Sobolev spaces and show that the equations are globally well-posed on the supports of these measures, respectively. Moreover, these measures are invariant under the flows that are constructed. Therefore, the constructed solutions are recurrent in time. Also, we show slow growth control on the time evolution of the solutions. A generalization to any… CONTINUE READING

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