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Creators/Authors contains: "Huang, Jiaxi"

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  1. ; (, Archive for Rational Mechanics and Analysis)
    Abstract The skew mean curvature flow is an evolution equation forddimensional manifolds embedded in$${\mathbb {R}}^{d+2}$$ R d + 2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In an earlier paper, the authors introduced a harmonic/Coulomb gauge formulation of the problem, and used it to prove small data local well-posedness in dimensions$$d \geqq 4$$ d ≧ 4 . In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension$$d\geqq 2$$ d ≧ 2 . This is achieved by introducing a new, heat gauge formulation of the equations, which turns out to be more robust in low dimensions. 
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  2. ; ; (, International Mathematics Research Notices)
    Abstract The skew mean curvature flow is an evolution equation for a $$d$$ dimensional manifold immersed into $$\mathbb {R}^{d+2}$$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature flow in dimensions $$d\geq 4$$. This extends the local well-posedness result in [7]. 
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  3. ; (, Communications in Mathematical Physics)
    Abstract The skew mean curvature flow is an evolution equation forddimensional manifolds embedded in$${{\mathbb {R}}}^{d+2}$$ R d + 2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension$$d\ge 4$$ d ≥ 4 . 
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