Continuity of the solution map to some active scalar equations in Hölder and Zygmund spaces
Abstract
We prove that the solution map for a family of non-linear transport equations in R n {\mathbb {R}}^n with a velocity field given by the convolution of the density with a kernel that is smooth away from the origin and homogeneous of degree − ( n − 1 ) -(n-1) is continuous in both the little Hölder class and the little Zygmund class. For particular choices of the kernel, one recovers well-known equations such as the 2D Euler or the 3D quasi-geostrophic equations.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 1105–1115
- Publication date
- 14 January 2026
- Language
- EN