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UID:1fb46639f2c3a33e566bd5e34acc9796
CATEGORIES:Nonlinear Analysis
CREATED:20240831T154846
SUMMARY:Changfeng Gui:   On a classification of steady solutions to two-dimensional Euler equations
LOCATION:Hill 705
DESCRIPTION:<p>Abstract: &nbsp;</p><p style="margin: 0px; font-style: normal; font-weig
 ht: normal; font-size: 11px; line-height: normal; font-family: Menlo; color
 : #000000;">In this talk, I shall provide a classification of steady soluti
 ons to two-dimensional incompressible</p><p style="margin: 0px; font-style:
  normal; font-weight: normal; font-size: 11px; line-height: normal; font-fa
 mily: Menlo; color: #000000;">Euler equations in terms of the set of flow a
 ngles. The first main result asserts that the set of flow angles of any bou
 nded steady flow in the whole plane must be the whole circle unless the flo
 w is a parallel shear flow. In an infinitely long horizontal strip or the u
 pper half-plane supplemented with slip boundary conditions, besides the two
  types of flows appeared in the whole space case, there exists an additiona
 l class of steady flows for which the set of flow angles is either the uppe
 r or lower closed semicircles. This type of flows is proved to be the class
  of non-shear flows that have the least total curvature. As consequences, w
 e obtain Liouville-type theorems for two-dimensional semilinear elliptic eq
 uations with only bounded and measurable nonlinearity, and the structural s
 tability of shear flows whose all stagnation points are not inflection poin
 ts, including Poiseuille flow as a special case. Our proof relies on the an
 alysis of some quantities related to the curvature of the streamlines. This
  talk is based on a joint work with Huan Xu and Chunjing Xie.</p><p>&nbsp;<
 /p><p><a href="https://sites.math.rutgers.edu/~yyli/NonlinearAnalysisSemina
 r.html">https://sites.math.rutgers.edu/~yyli/NonlinearAnalysisSeminar.html<
 /a></p><p>&nbsp;</p>
CONTACT:University of Macau
DTSTAMP:20260829T164805
DTSTART;TZID=America/New_York:20240917T134000
DTEND;TZID=America/New_York:20240917T144000
SEQUENCE:0
TRANSP:OPAQUE
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