Dynamics of Partial Differential Equations

Volume 10 (2013)

Number 4

Major open problems in chaos theory, turbulence and nonlinear dynamics

Pages: 379 – 392

DOI: http://dx.doi.org/10.4310/DPDE.2013.v10.n4.a5

Author

Y. Charles Li (Department of Mathematics, University of Missouri, Columbia, Mo., U.S.A.)

Abstract

Nowadays, chaos theory, turbulence and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence (chaos and turbulence engineering), 2. rough dependence on initial data – short term unpredictability (turbulence physics), 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.

Keywords

chaos, turbulence, effective description of chaos and turbulence, rough dependence on initial data, short term unpredictability, arrow of time, enrichment paradox, pesticide paradox, plankton paradox

2010 Mathematics Subject Classification

Primary 37-xx, 70-xx, 76-xx, 92-xx. Secondary 34-xx, 35-xx, 80-xx, 82-xx.

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