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Symplectic non-squeezing for the cubic NLS on the plane

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Symplectic non-squeezing for the cubic NLS on the plane
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9
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21
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
We prove that the flow of the cubic NLS in two dimensions cannot squeeze a ball in $L^2$ into a cylinder of lesser radius. This is a PDE analogue of Gromov's non-squeezing theorem for an infinite-dimensional Hamiltonian PDE in infinite volume. It is joint work with R. Killip and X. Zhang