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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:Abstract:  \nIn this talk, I shall provide a classification of steady solut
 ions to two-dimensional incompressible\nEuler equations in terms of the set
  of flow angles. The first main result asserts that the set of flow angles 
 of any bounded steady flow in the whole plane must be the whole circle unle
 ss the flow is a parallel shear flow. In an infinitely long horizontal stri
 p or the upper half-plane supplemented with slip boundary conditions, besid
 es the two types of flows appeared in the whole space case, there exists an
  additional class of steady flows for which the set of flow angles is eithe
 r the upper 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 conse
 quences, we obtain Liouville-type theorems for two-dimensional semilinear e
 lliptic equations with only bounded and measurable nonlinearity, and the st
 ructural stability of shear flows whose all stagnation points are not infle
 ction points, including Poiseuille flow as a special case. Our proof relies
  on the analysis of some quantities related to the curvature of the streaml
 ines. This talk is based on a joint work with Huan Xu and Chunjing Xie.\n \
 nhttps://sites.math.rutgers.edu/~yyli/NonlinearAnalysisSeminar.html (https:
 //sites.math.rutgers.edu/~yyli/NonlinearAnalysisSeminar.html)\n \n
X-ALT-DESC;FMTTYPE=text/html:<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:20260829T034551
DTSTART;TZID=America/New_York:20240917T134000
DTEND;TZID=America/New_York:20240917T144000
SEQUENCE:0
TRANSP:OPAQUE
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