PROBLEMS ON THE HYDRODYNAMIC LIMIT AND RELATED TOPICS

流体力学极限问题及相关主题

• 批准号: 15540109
• 负责人: UCHIYAMA Kohei
• 金额: $ 2.18万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540109/
• 关键词: hydrodynamic limit; spectral gap; non-gradient system; principle of large deviations; fluctuation process; 流体力学; スケール極限; 排他過程; ランダムウォーク; Green関数; 局所平衡; スケーリング極限; 相対エントロピー; hydrodynamic limit; equilibrium fluctuation; spectral gap; non-line

In 2003 introducing a lattice gas model, called zero-range-exclusion model, which possesses two conservative quantities, we obtained an estimate of the spectral gap for the model [cf. An estimate of the spectral gap for zero-range-exclusion dynamics, Osaka Jour.Math. 141(no.4) (2004)]. This model is of non-gradient type and its spin values are unbounded so that there arise various interesting problems in the investigation of the hydrodynamic limit for the model.The estimate obtained, though not uniform in the density of the gas as those for many known models are, seems sufficiently accurate for dealing with the problems concerning its hydrodynamic limit. In fact based on our estimate we proved in 2004 that the fluctuations around the hydrodynamic scaling in the equilibrium converge to a process that is characterized as an infinite dimensional Ornstein-Uhlenbeck prosess [cf. Equilibrium fluctuations for zero-range-exclusion processes, Jour.Stat.Phys. (2004)]. We encountered a certain difficulty for proving the tightness of a sequence of the processes of finite size and resolved it by devising a trick by using a time reversed process.

2003年，我们引入了具有两个保守量的零范围排斥模型的晶格气体模型，我们获得了模型的光谱间隙的估计。零范围排斥动力学的光谱差距的估计值，大阪日记。 141（No.4）（2004）]。该模型是非梯度类型的，其自旋值是无限的，因此在研究模型的流体动力学限制时会出现各种有趣的问题。尽管在许多已知模型的气体密度中，获得的估计值似乎并不均匀，但似乎足够准确地处理了与其流体动力学极限有关的问题。实际上，基于我们的估计，我们在2004年证明了平衡中流体动力缩放的波动融合到一个被表征为无限尺寸的Ornstein-Ornstein-Uhlenbeck Prosess的过程[CF。零范围排斥过程的平衡波动，jour.stat.phys。 （2004）]。我们遇到了一定的困难，以证明有限大小的一系列过程的紧密度，并通过使用时间逆转过程来设计技巧来解决它。

项目成果

Heat escape

热量逸出

• 发表时间: 2003
• 期刊: Math. Ann. 327
• 作者: Kazuhiro Kurata;M.Maniwa;Kazuhiro Kurata;Minoru Murata
• 通讯作者: Minoru Murata

Uniqueness theorems for parabolic equations and Martin BOUNDARY for elliptic equations in skew producl form

抛物线方程的唯一性定理和斜积形式椭圆方程的 Martin BOUNDARY

• 发表时间: 2005
• 期刊: J.Math.SOC.Japan 57
• 作者: H.Matsuzoe;J.Inoguchi;蔵野 正美;M.MURATA
• 通讯作者: M.MURATA

Uniqueness theorems for parabolic equations and Martin BOUNDARY for elliptic equations in skew product form

抛物线方程的唯一性定理和斜积形式椭圆方程的 Martin BOUNDARY

• 发表时间: 2005
• 期刊: J.Math.Soc.Japan 57
• 作者: M.Murata

Tatsuo Iguchi: "On steady surface waves over a periodic bottom : relations between the pattern of imperfect bifurcation and the shape of the bottom"Wave Motion. 37・3. 219-239 (2003)

Tatsuo Iguchi：“关于周期性底部的稳定表面波：不完美分叉模式与底部形状之间的关系”37・3（2003）。

Zero range exclusion particle systems

零距离排除粒子系统

• 发表时间: 2004
• 期刊: Adv,Stud.Pure Math 39
• 作者: Yoshida;Y.;Yasuda;M.;Nakagami;T.;Kurano;M.;酒井政美;K.UCHIYAMA
• 通讯作者: K.UCHIYAMA