Well-posedness of the equation for the three-form field in the eleven\n dimensional supergravity

2010/10/04 by Boris Ettinger, Ettinger, Boris
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35L05 (Primary) 70S20 #83E50 (Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1010.0648

openalex publication_date 2010/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the equations for the three-form field - a system of semi-linear\ngauge-invariant wave equations which arises in the theory of eleven dimensional\nsupergravity. We prove that the Cauchy problem is well-posed globally in time\nfor the fixed-gauge version of the equation for a small compactly supported\nsmooth data. We employ the method of Klainerman vector fields along with a\nfiner analysis of the nonlinearity to establish an integrable decay in the\nenergy estimate.\n

Related

• Local well-posedness for the (n+1)-dimensional Maxwell-Klein-Gordon equations in temporal gauge
• Unconditional global well-posedness in energy space for the\n Maxwell-Klein-Gordon system in temporal gauge
• The superspace formulation of eleven-dimensional supergravity with a seven-form
• Simple Supergravity pp-Waves
• Low regularity local well-posedness for the Maxwell-Klein-Gordon\n equations in Lorenz gauge