Bilinear Strichartz estimates for the Schrödinger map problem

2012/10/18 by Benjamin Dodson, Dodson, Benjamin · 1 citation
Mathematics · #35B33 #35Q55 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1210.5255

openalex publication_date 2012/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove bilinear Strichartz estimates for a solution to the Schrödinger map problem whose size is small in the critical Strichartz space | |∇|^{(d - 2)/(2)} ψ_x |_L_t,x^{(2(d + 2))/(d)}. These estimates will be useful in an upcoming paper in proving a local well - posedness result. Bilinear estimates make use of an argument similar to the argument found in Planchon and Vega (2009). We use the same gauges as in Bejenaru, Ionescu and Kenig (2007), Bejenaru et al. (2011), and Smith.

Citations

• Global well-posedness for 2D radial Schrödinger maps into the sphere
• Global regularity of wave maps III. Large energy from \R¹⁺² to hyperbolic spaces

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• Schrödinger maps to a Kähler manifold in two dimensions

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