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On the nonuniqueness of weak solution of the Euler equation
Author(s) -
Shnirelman A.
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199712)50:12<1261::aid-cpa3>3.0.co;2-6
Subject(s) - mathematics , euler's formula , torus , mathematical analysis , interval (graph theory) , euler equations , zero (linguistics) , momentum (technical analysis) , backward euler method , pure mathematics , combinatorics , geometry , linguistics , philosophy , finance , economics
Weak solution of the Euler equations is defined as an L 2 ‐vector field satisfying the integral relations expressing the mass and momentum balance. Their general nature has been quite unclear. In this work an example of a weak solution on a 2‐dimensional torus is constructed that is identically zero outside a finite time interval. This example is simpler and more transparent than the previous example of V. Scheffer (J. Geom. Anal. 3(4), 1993, pp. 343–401). © 1997 John Wiley & Sons, Inc.