Maximal Double-Exponential Growth for the Euler Equation on the Half-Plane

2025/07/06 by Andrej Zlatoš, Zlatos, Andrej · 2 citations
Mathematics · #35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2507.04198

openalex publication_date 2025/07/06 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

Abstract

We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are the first such results on an unbounded resp. any 2D domain.

Citations

• Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole
• Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow
• Exponential growth of the vorticity gradient for the Euler equation on the torus
• Small scale creation for solutions of the incompressible two dimensional Euler equation
• Double exponential growth of the vorticity gradient for the two-dimensional Euler equation

Cited by

• Stability of Lamb dipoles for odd-symmetric and non-negative initial disturbances without the finite mass condition
• Superlinear gradient growth for 2D Euler equation without boundary

Related

• Double exponential growth of the vorticity gradient for the two-dimensional Euler equation
• Small scale creation for solutions of the incompressible two dimensional Euler equation
• Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow
• Superlinear gradient growth for 2D Euler equation without boundary
• Infinite-time Exponential Growth of the Euler Equation on Two-dimensional Torus