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

2012/02/15 by Jun‐ichi Segata, Jun-ichi Segata, Segata, Jun-ichi
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1202.3211

arxiv created 2012/02/15 · openalex publication_date 2012/02/15 · arxiv updated 2012/02/16 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

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).

Citations

• Nonlocal models for nonlinear, dispersive waves

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