Short-time regular solutions exist for m≤3 and global weak solutions exist for all m≥1 for the incompressible Schrödinger flow from smooth bounded domains into S^2.
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Existence of weak solutions and regular solutions to the incompressible Schr\"odinger flow
Short-time regular solutions exist for m≤3 and global weak solutions exist for all m≥1 for the incompressible Schrödinger flow from smooth bounded domains into S^2.