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Monotonicity Method Applied to the Complex Ginzburg–Landau and Related Equations

✍ Scribed by Noboru Okazawa; Tomomi Yokota

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
141 KB
Volume
267
Category
Article
ISSN
0022-247X

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✦ Synopsis

Global existence of unique strong solutions is established for the complex Ginzburg-Landau equation

The key is a new inequality in monotonicity methods. It is based on the sectorial estimates of -in L p+1 and the nonlinear operator u → u p-1 u appearing in the equation. The key inequality also yields the global existence of unique strong solutions of the nonlinear Schrödinger type equation with monotone nonlinearity ∂ t u -i u + u p-1 u = 0 for all p ≥ 1.  2002 Elsevier Science (USA)

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