Low regularity well-posedness for the 3D Klein-Gordon-Schr "odinger\n system

2010/11/13 by Hartmut Pecher, Pecher, Hartmut · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1011.3128

openalex publication_date 2010/11/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The Klein-Gordon-Schr "odinger system in 3D is shown to be locally well-posed\nfor Schr "odinger data in H^s and wave data in H^\σ \× H^{\σ -1},\nif s > - 1/4, \σ > - 1/2, \σ -2s > 3/2 and \σ -2 < s < \σ +1 .\nThis result is optimal up to the endpoints in the sense that the local flow map\nis not C² otherwise. It is also shown that (unconditional) uniqueness holds\nfor s=\σ=0 in the natural solution space C⁰([0,T],L²) \×\nC⁰([0,T],L²) \× C⁰([0,T],H^-1/2) . This solution exists even globally\nby Colliander, Holmer and Tzirakis. The proofs are based on new well-posedness\nresults for the Zakharov system by Bejenaru, Herr, Holmer and Tataru, and\nBejenaru and Herr.\n

Cited by

• Large Time Behavior of the Klein-Gordon-Schrödinger system

Related

• Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
• Some new well-posedness results for the Klein-Gordon-Schr "odinger\n system
• Local well-posedness for the Klein-Gordon-Zakharov system in 3D
• Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on \mathbb R⁺
• Well-posedness results for a generalized Klein-Gordon-Schrödinger system