Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus

Details Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus

2012-02-15

arxiv.org/abs/1202.3211v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the time local and global well-posedness for the fourth order
nonlinear Schrodinger type equation (4NLS) on the torus. The nonlinear term of
(4NLS) contains the derivatives of unknown function and this prevents us to
apply the classical energy method. To overcome this difficulty, we introduce
the modified energy and derive an a priori estimate for the solution to (4NLS).

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