Damped infinite energy solutions of the 3D Euler and Boussinesq equations


We revisit a family of infinite-energy solutions of the 3D incompressible Euler equations proposed by Gibbon et al. [9] and shown to blowup in finite time by Constantin [6]. By adding a damping term to the momentum equation we examine how the damping coefficient can arrest this blowup. Further, we show that similar infinite-energy solutions of the inviscid 3D Boussinesq system with damping can develop a singularity in finite time as long as the damping effects are insufficient to arrest the (undamped) 3D Euler blowup in the associated damped 3D Euler system.

Journal of Differential Equations, 265 (9): 3841-57
William Chen
William Chen
Ph.D. Student in Economics

I am a Ph.D. student in Economics at MIT. I am also a former Senior Research Analyst of the DSGE Team at the Federal Reserve Bank of New York. My research interests include macroeconomics, finance, and computational macroeconomics. Within these fields, I am particularly interested in business cycle theory, financial crises, and macro-labor. My pronouns are he/him.