The nonlinear Schrodinger equation
is said to be mass critical since the scaling u(t,x)=l-d/2
u(t/l2
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, x/l) preserves the L2
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- norm, m = ± 1. In this talk we will discuss the concentration compactness method, which is used to prove global well - posedness and scattering for (1) for all initial data u(0) in L2
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(Rd
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) when m = +1, and for u(0) having L2
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norm below the ground state when m = -1. This result is sharp.
As time permits the talk will also discuss the energy - critical problem in Rd \ W,
where W is a compact, convex obstacle. [video]
Generated at 2:20am Wednesday, April 24, 2024 by Mcal. Top
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