Professor Vladimir Sverak

CSENG Mathematics, School of
College of Science & Engineering
Twin Cities
Project Title: 
Regularity of Solutions of Fundamental Equations of Fluid Mechanics

This project studies the open problem of regularity of solutions of the 3D incompressible Euler's equation. One of the fundamental equations of fluid mechanics, the equation was first introduced in 1755. However,  it remains open to this day whether the equation is self-consistent from the point of view of Newtonian mechanics: given any smooth initial velocity field on the fluid, which (in the case of constant density assumed here) represents complete information about the system in the Newtonian sense, does the equation unambiguously predict what will happen with the fluid in a fture time? While the answer is known to be positive for short times, it is not clear whether it will be positive for longer times, due to possible singularity formation.

Recently, new exiting scenarios have been published for possible singularities, and these researchers plan to use numerical calculations to investigate further the potential singularities suggested by this work. The researchers have made good progress in confirming some new ideas about possible singularity formation, and are continuing work on verification of certain specific scenarios.

The researchers have made good progress in confirming some new ideas about possible singularity formation, and they are involved in various verifications, such as resolution study, etc. Much of the work of in 2019 concerned resolutions studies and improving the code, to obtain a maximal resolution with the given resources. 

Project Investigators

Guo Luo
Professor Vladimir Sverak
 
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