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Almost conservation laws and global wellposedness


Speaker: James Colliander, UC Berkeley
Location: 693 Kerr
Start time: Mon, Jan 29 2001, 4:10PM

A dynamical reinterpretation of the L^2 mass conservation law for solutions of the KdV equation has led to a general procedure for proving almost conservation laws for solutions of nonlinear Hamiltonian PDE. The almost conserved quantities have been used to globalize the available local-in-time wellposedness results for various KdV and NLS type equations and will provide insights into the long-time behavior of solutions. This talk will survey the known local theory, highlighting aspects requiring further investigation. The procedure for constructing almost conserved quantities will be described.