Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.
ArXiv:2302.09969 (2023)
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Global large solutions exist for incompressible MHD equations with small Alfvén numbers when viscosity and resistivity are both positive.
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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Low-regularity Schr\"odinger map flow on high-dimensional periodic domains
Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.
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On Global-in-time Solutions of Incompressible MHD Equations with Small Alfv\'en Numbers
Global large solutions exist for incompressible MHD equations with small Alfvén numbers when viscosity and resistivity are both positive.
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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.