\u6d41\u3000\u4f53\u3000\u529b\u3000\u5b66\u3000\u30bb\u3000\u30df\u3000\u30ca\u3000\u30fc<\/p>\n
(\u4eac\u90fd\u5927\u5b66\u5fdc\u7528\u6570\u5b66\u30bb\u30df\u30ca\u30fc(KUAMS)\u3068\u306e\u5171\u50ac)<\/p>\n
\u65e5\u6642:\u00a0 \uff19\u6708\uff11\uff14\u65e5\uff08\u91d1\uff09 \uff11\uff15\uff1a\uff10\uff10 \u304b\u3089 \uff11\uff16\uff1a\uff13\uff10<\/p>\n
\u5834\u6240:\u00a0 \u4eac\u5927 \u7406\u5b66\u7814\u7a76\u79d1 \u7269\u7406\u5b66\u6559\u5ba4(\u7406\uff15\u53f7\u9928)\u3000\uff14\uff10\uff11\u53f7\u5ba4<\/p>\n
\u8b1b\u5e2b\uff1a Uriel Frisch \u6c0f
\nLaboratoire Lagrange, Observatoire and Universite Cote d’Azur
\nNice, France<\/p>\n
\u8b1b\u6f14\u984c\u76ee\uff1aThe mathematical and numerical construction of
\nturbulent solutions for the 3D incompressible Euler
\nequation and its perspectives<\/p>\n
\u8b1b\u6f14\u8981\u65e8\uff1a<\/p>\n
Starting with Kolmogorov\u2019s 1941 (K41) work, infinite Reynolds number
\nflow is known to have velocity increments over a small distance r that
\nvary roughly as the cubic root of r. Formally,\u00a0 such\u00a0 flow\u00a0 is\u00a0 expected\u00a0 to
\nsatisfy\u00a0 Euler\u2019s\u00a0 partial differential\u00a0 equation,\u00a0 but\u00a0 the\u00a0 flow\u00a0 being
\nnot\u00a0 spatially differentiable, the equation is satisfied only in
\na distributional sense. Since Leray\u2019s 1934 work, such solutions are called
\nweak. Actually\u00a0 they\u00a0 were\u00a0 already\u00a0 present\u00a0 \u2013very\u00a0 briefly\u2013\u00a0 in
\nLagrange\u2019s 1760\/1761 work on non-smooth solutions of the wave equation.
\nA\u00a0 major\u00a0 breakthrough\u00a0 has\u00a0 happened\u00a0 recently: mathematicians\u00a0 succeeded
\nin\u00a0 constructing\u00a0 rigourously\u00a0 weak solutions\u00a0 of\u00a0 the\u00a0 Euler\u00a0 equation
\nwhose\u00a0 spatial\u00a0 regularity\u00a0 \u2013measured by their H\u00f6lder continuity exponent\u2013
\nis arbitrarily close to the value predicted by K41 (Isett 2018), Buckmaster et
\nal. 2017). Furthermore these solutions present the anomalous energy dissipation
\ninvestigated by Onsager in 1949 (Ons49). We shall highlight some aspects of
\nthe derivation of these results which took about ten years and was started
\noriginally by Camillo de Lellis and Laszlo Szekelyhidi and continued with a
\nnumber\u00a0 of\u00a0 collaborators.\u00a0 On\u00a0 the\u00a0 mathematical\u00a0 side\u00a0 the derivation makes
\nuse of techniques developed by Nash (1954) for isometric embedding and by Gromov
\n(1986, 2017) for convex\u00a0 integration.\u00a0 Fortunately,\u00a0 many\u00a0 features\u00a0 of\u00a0 the
\nderivation\u00a0 have\u00a0 a\u00a0 significant\u00a0 fluid\u00a0 mechanical\u00a0 content.\u00a0 In particular
\nthe successive introduction of finer and finer flow structures, called Mikados
\nby Daneri and Szekelyhidi (2017) because\u00a0 they\u00a0 are\u00a0 slender\u00a0 and jetlike.
\nThe Mikados generate Reynolds stresses on larger scales; they can be chosen
\nto cancel discrepancies between approximate and exact solutions of the Euler
\nequation. A particular engaging aspect of the construction of weak solutions
\nis its flexibility. The Mikados can be chosen not only to\u00a0 reproduce\u00a0 K41\/Ons49
\nselfsimilar\u00a0 turbulence,\u00a0 but\u00a0 also\u00a0 to synthesize\u00a0 a\u00a0 large\u00a0 class\u00a0 of
\nturbulent\u00a0 flows,\u00a0 possessing,\u00a0 for example,\u00a0 small-scale\u00a0 intermittency
\nand\u00a0 multifractal\u00a0 scaling. This huge playground must of course be explored
\nnumerically for testing all manners of physical phenomena and theories, a
\nprocess being started in a collaboration between Leipzig, Nice, Kyoto and Rome.<\/p>\n
(in collaboration with\u3000Laszlo Szekelyhidi,Department of Mathematics,
\nUniversity of Leipzig, Germany\u3000and\u3000Takeshi Matsumoto,Department of
\nPhysics, Kyoto University, Japan)<\/p>\n
+–+–+–+–+–+–+–+–+–+–
\n\u4e16\u8a71\u4eba\uff1a\u5c71\u7530 \u9053\u592b(\u4eac\u5927\u6570\u7406\u7814)\uff0c \u7af9\u5e83 \u771f\u4e00\uff08\u4eac\u5927\u6570\u7406\u7814\uff09\uff0c
\n\u85e4 \u5b9a\u7fa9(\u4eac\u5927\u7406)\uff0c\u677e\u672c \u525b(\u4eac\u5927\u7406)
\n\u9023\u7d61\u5148\uff1a\u5c71\u7530\u9053\u592b\u00a0yamada_at_kurims.kyoto-u.ac.jp
\n==============================
\u6d41\u3000\u4f53\u3000\u529b\u3000\u5b66\u3000\u30bb\u3000\u30df\u3000\u30ca\u3000\u30fc (\u4eac\u90fd\u5927\u5b66\u5fdc\u7528\u6570\u5b66\u30bb\u30df\u30ca\u30fc(KUAMS)\u3068\u306e\u5171\u50ac) \u65e5\u6642:\u00a0 \uff19\u6708\uff11\uff14\u65e5\uff08\u91d1\uff09 \uff11\uff15\uff1a\uff10\uff10 \u304b\u3089 \uff11\uff16\uff1a\uff13\uff10 \u5834\u6240:\u00a0 \u4eac\u5927 \u7406\u5b66\u7814\u7a76\u79d1 \u7269\u7406\u5b66\u6559\u5ba4(\u7406\uff15\u53f7\u9928)\u3000\uff14\uff10\uff11\u53f7\u5ba4 \u8b1b\u5e2b\uff1a Uri […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,50],"tags":[],"class_list":["post-1002","post","type-post","status-publish","format-standard","hentry","category-16","category-50"],"_links":{"self":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1002","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1002"}],"version-history":[{"count":3,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1002\/revisions"}],"predecessor-version":[{"id":1006,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1002\/revisions\/1006"}],"wp:attachment":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1002"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1002"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}