ON THE SCHRODINGER-DEBYE SYSTEM IN COMPACT RIEMANNIAN MANIFOLDS

Author(s)

Nogueira, Marcelo ^[1] ; Panthee, Mahendra ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS; v. 19, n. 1, p. 425-453, JAN 2020.
• Web of Science Citations: 0

Abstract

We consider the initial value problem (IVP) associated with the Schriidinger-Debye system posed on a d-dimensional compact Riemannian manifold M and prove the local well-posedness result for given data (u(0),v(0)) is an element of H-s(M) x (H-s (M) boolean AND L-infinity(M)) whenever s > d/2- 1/2, d >= 2. For d = 2, we apply a sharp version of the Gagliardo-Nirenberg inequality in compact manifold to derive an a priori estimate for the H-1-solution and use it to prove the global well-posedness result in this space. (AU)

• FAPESP's process: 16/25864-6 - Nonlinear Evolution Equations of Dispersive Type
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants