VARGA KALANTAROV 60.
YAŞGÜNÜ TOPLANTISI
5 Kasım 2010
Koç Üniversitesi
Konuşmacılar
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Okay Çelebi |
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Yeditepe Üniversitesi |
|
Alp Eden |
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Boğaziçi Üniversitesi |
|
Gregory Seregin |
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Oxford Üniversitesi |
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Mete Soner |
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ETH - Zürih |
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Edriss
Titi |
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UC Irvine – Weizmann Inst. |
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Ali Ülger |
|
Koç Üniversitesi |
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Bu konferans Koç Üniversitesi ve Tübitak Projesi 107T896 tarafından desteklenmektedir. |
|
Her türlü sorunuz için lütfen kalantarov60@gmail.com
adresine e-posta atınız. |
Program
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9:30 |
Açılış Konuşmaları |
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9:45 |
Okay Çelebi |
Varga’yı ne kadar tanıyorsunuz? |
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10:30 |
Ara |
|
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11:00 |
Ali Ülger |
Türkiye’de Matematik Niçin Gelişemedi? |
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11:45 |
Ara |
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12:00 |
Alp Eden |
Remarks
on the asymptotic behavior of the solutions of non-linear PDEs |
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12:45 |
Öğle Yemeği |
|
|
14:00 |
Gregory Seregin |
Local
Regularity Theory for the Navier-Stokes Equations |
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15:00 |
Ara |
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15:30 |
Edriss Titi |
On the
Loss of Regularity for the Three-Dimensional Euler Equations |
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16:30 |
Ara |
|
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17:00 |
Mete Soner |
Discrete
approximations of nonlinear parabolic equations from finance |
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18:00 |
Konferans Yemeği |
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Konuşmalar
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Okay Çelebi - Varga’yı ne kadar tanıyorsunuz? |
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|
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Ali Ülger - Türkiye’de Matematik Niçin Gelişemedi? |
|
|
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Alp
Eden - Remarks on the asymptotic behavior of the solutions of non-linear PDEs |
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TBA |
|
|
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Gregory
Seregin - Local Regularity Theory for the Navier-Stokes
Equations |
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In the
talk, I am going to discuss recent regularity results for suitable weak
solutions to the Navier-Stokes equations. |
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|
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Edriss Titi - On the Loss of Regularity for the
Three-Dimensional Euler Equations |
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A basic example of shear flow was introduced by DiPerna
and Majda to study the weak limit of oscillatory
solutions of the Euler equations of incompressible ideal fluids. In
particular, they proved by means of this example that weak limit of solutions
of Euler equations may, in some cases, fail to be a solution of Euler
equations. We use this shear flow example to provide non-generic, yet
nontrivial, examples concerning the loss of smoothness of solutions of the
three-dimensional Euler equations, for initial data that do not belong to
$C^{1,\alpha}$. Moreover, we show by means of this shear flow example the
existence of weak solutions for the three-dimensional Euler equations with vorticity that is having a nontrivial density
concentrated on non-smooth surface. This is very different from what has been
proven for the two-dimensional Kelvin-Helmholtz problem where a minimal
regularity implies the real analyticity of the interface. Eventually, we use this shear flow to provide
explicit examples of non-regular solutions of the three-dimensional Euler
equations that conserve the energy, an issue which is related to the Onsager
conjecture. |
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|
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Mete Soner - Discrete approximations of nonlinear parabolic
equations from finance |
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It is known that scalar, parabolic, semi-linear partial differential equations have several probabilistic representations. Also "recently" we were able to obtain a representation for fully nonlinear equations and geometric equations as well. Reversely, one can derive these equations as pricing equations for some financial models. One such occasion is a liquidity model which yields a quadratic nonlinearity of the Hessian. In joint work with Selim Gokay, we used this model to understand the discretization properties of such representations. In this talk, I will describe this simple discrete financial model and the convergence proof. |