Partial Differential Equations
Parabolic partial differential equations may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The Ginzburg–Landau, the Kuramoto–Sivashinsky, and the two-dimensional, forced Navier–Stokes equations are all known to have global attractors of finite dimension.
For the three-dimensional, incompressible Navier–Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.
Read more about this topic: Attractor
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... (1972) Ennio de Giorgi 1996 ... Maths He was an Italian mathematician,who worked on partial differential equations ... Hilbert problem on the regularity of solutions of elliptic partial differential equations ... and physicist, known for Theory of integral equations and the Lotka–Volterra equations Maria Montessori 1952 ... Natural sciences Founder of the Montessori method of education Charles Ponzi 1949 ... Known for the ...
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