Time: 1:30 July 19th, 2019
Place: Room No. 301, No. 3 Building, Xuhui Campus
Speaker: Professor ROBIN MING CHEN,University of Pittsburgh
Robin Ming Chen completed his PhD at Brown University in 2007 under the supervision of Walter Strauss. He joined University of Pittsburgh in 2011. Chen works in the area of nonlinear PDEs, particularly those arising from fluid mechanics, geophysics, and materials. A large part of Chen’s work has been devoted to the study of the global regularity and singularity formation of solutions, the existence and qualitative properties of traveling waves, and the stability and instability of traveling waves.
We consider 2D steady water waves with heterogeneous density. The presence of stratification allows for a wide variety of traveling waves. We prove that for any smooth choice of upstream velocity and monotone streamline density function, there always exists a continuous curve of solitary waves with large amplitude, which are even and decreasing monotonically on either side of a central crest. As one moves along this curve, the horizontal fluid velocity comes arbitrarily close to the wave speed.