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UID:news1793@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20250423T135528
DTSTART;TZID=Europe/Zurich:20250430T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Wojciech Ozanski (Florid
 a State University)
DESCRIPTION:We are concerned with the ideal magneto-hydrodynamic system of 
 PDEs posed on a domain in $\\mathbb{R}^2$ or $\\mathbb{R}^3$\, such that a
  part $\\Gamma $ of the boundary of the domain is controlled in the sense 
 that $v\\cdot n = k\, b\\cdot n =l$ on $\\Gamma$\, where $k\,l$ are contro
 ls\, and $v$ and $b$ denote the velocity field and the magnetic field of t
 he system\, respectively. The aim of the control is to bring the system fr
 om a given initial state $(v_0\,b_0)$ into a given final state $(v_1\,b_1)
 $ in finite time. Such a controllability problem was resolved for the 2D a
 nd 3D incompressible Euler equation in the 1990's by Coron and Glass. The 
 case of the ideal MHD system is much harder due to the lack of the pressur
 e function in the equation for $b$. Very recently\, exact boundary control
 lability of the 2D MHD system was achieved in the case of a flat channel b
 y Kukavica\, Novack\, Vicol. In the talk we will discuss the main difficul
 ties of the problem and present a recent result (joint with Kukavica)\, wh
 ich completely resolves the case of any domain in both 2D and 3D incompres
 sible ideal MHD system.
X-ALT-DESC:<p>We are concerned with the ideal magneto-hydrodynamic system o
 f PDEs posed on a domain in $\\mathbb{R}^2$ or $\\mathbb{R}^3$\, such that
  a part $\\Gamma $ of the boundary of the domain is controlled in the sens
 e that $v\\cdot n = k\, b\\cdot n =l$ on $\\Gamma$\, where $k\,l$ are cont
 rols\, and $v$ and $b$ denote the velocity field and the magnetic field of
  the system\, respectively. The aim of the control is to bring the system 
 from a given initial state $(v_0\,b_0)$ into a given final state $(v_1\,b_
 1)$ in finite time. Such a controllability problem was resolved for the 2D
  and 3D incompressible Euler equation in the 1990's by Coron and Glass. Th
 e case of the ideal MHD system is much harder due to the lack of the press
 ure function in the equation for $b$. Very recently\, exact boundary contr
 ollability of the 2D MHD system was achieved in the case of a flat channel
  by Kukavica\, Novack\, Vicol. In the talk we will discuss the main diffic
 ulties of the problem and present a recent result (joint with Kukavica)\, 
 which completely resolves the case of any domain in both 2D and 3D incompr
 essible ideal MHD system.</p>
DTEND;TZID=Europe/Zurich:20250430T160000
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