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Asymptotically Stable Ill-Posedness of Geometric Quasilinear Wave Equations
Başlık:
Asymptotically Stable Ill-Posedness of Geometric Quasilinear Wave Equations
Yazar:
Granowski, Ross, author.
ISBN:
9780438047716
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (131 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Sergiu Klainerman Committee members: Mihalis Dafermos; Alexandru Ionescu.
Özet:
We show that the recent work of Speck, Holzegel, Luk and Wong in [18] on nearly plane symmetric shock formation is intimately connected to the low-regularity illposedness of geometric quasilinear wave equations in H3 x H2( R3). Indeed, as with shock formation, this is actually a generic phenomenon: for almost all (g-1)alphabeta (phi) which are perturbations of the Minkowski metric we can specify initial data which is arbitrarily small in H2 x H1(R3) but whose H1 energy blows up arbitrarily fast in the domain of future dependence of the data. We demonstrate that illposedness is actually a corollary of the nearly planar shock formation theorem in 3+1 dimensions. The nearly planar shock formation result actually gives us even more: the stability of the breakdown under asymptotically small perturbations of ``Lindblad-type" initial data. In other words, Lindblad's result is not simply an artifact of symmetry. We then show that the proof in [18] extends from 2+1 to 3+1 dimensions. This is largely the same argument, although elliptic estimates are now necessary to control some of the new top-order error terms which are nontrivial in the 3+1 dimensional setting. Our result demonstrates that the conjectural local well-posedness of the timelike minimal surface equation in H3 x H2( R3)is an exceptional case: every other equation in its class of irrotational, compressible relativistic fluid equations is illposed in H3 x H2( R3).
Notlar:
School code: 0181
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(681034.1) | 681034-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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