Quantitative Estimates for Regular Lagrangian Flows with BV Vector Fields

• Published in: Communications on pure and applied mathematics Vol. 74; no. 6; pp. 1129 - 1192
• Main Author: Nguyen, Quoc‐Hung
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.06.2021; John Wiley and Sons, Limited
• Subjects: Fields (mathematics); Kernels

This paper is devoted to the study of flows associated to non‐smooth vector fields. We prove the well‐posedness of regular Lagrangian flows associated to vector fields B = (B1, …, Bd) ∈ L1(ℝ+; L1(ℝd) + L∞(ℝd)) satisfying Bi=∑j=1mKji*bj, bj ∈ L1(ℝ+, BV(ℝd)) and div(B) ∈ L1(ℝ+; L∞(ℝd)) for d, m ≥ 2, w...