作者：Schramm, Oded; Sheffield, Scott
作者单位：Microsoft; New York University
摘要：We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain-with boundary values -lambda on one boundary arc and lambda on the complementary arc-the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are -a < 0 on the first arc and...
作者：Koch, Gabriel; Nadirashvili, Nikolai; Seregin, Gregory A.; Sverak, Vladimir
作者单位：University of Chicago; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University of Oxford; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study bounded ancient solutions of the Navier-Stokes equations. These are solutions with bounded velocity defined in R (n) x (-1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios...
