Mathematical Sciences: Study of Model Equations For Water Waves

9622858 Chen研究员将研究各种描述水波在非线性、色散介质中双向传播的Boussinesq系统。具有各种近似耗散项的Boussinesq系统也将从理论上和数值上进行研究。一般来说，对于著名的描述波在一个方向上传播的kdv方程所研究的所有问题，都应该进行研究。该项目的主要目标是确定哪种方程组和哪种耗散机制最适合于流体力学中物理问题的建模。理想的系统至少应该在数学上合理，物理上正确，具有最小的复杂性，并且可以用来模拟广泛的实际水波问题。

9622858 Chen The investigator will study various Boussinesq systems which describe the two-way propagation of water waves in nonlinear, dispersive media. Boussinesq systems with various approximate dissipative terms will also be studied theoretically and numerically. Generally speaking, all the issues studied for the famous KdV-equation, which describes waves traveling in one direction, should be investigated. The major goal for this project is to decide which system of equations and which dissipative mechanism is best suited for the modeling of physical problems in fluid mechanics. The ideal system should at least be mathematically sound, physically correct, have the least complexity, and can be used to simulate a wide range of real water wave problems.