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Centre's Silver Medal Winner Dr Tong Yang, Assistant Professor at City University of Hong Kong, was the proud recipient of one of four silver Morningside Medals presented at the first International Congress of Chinese Mathematicians held in Beijing in December 1998. He won the medal for his work in solving the well-posedness theory for hyperbolic conservation laws, of which the Euler equations for gas dynamics are some of the most famous examples. The theory on partial differential equations involves three problems: existence, stability and uniqueness. The existence theory was well established by James Glimm in 1965. However, stability and uniqueness remained open problems. What Dr Yang achieved was to solve these problems for the general system of hyperbolic conservation laws, with the tremendous help of his main collaborator, Prof Tai-Ping Liu of Stanford University. Dr Yang himself says that, though there remain other general functions and systems that still need working on, his work has undoubtedly gone a long way in opening up the field for further research. Dr Yang was first introduced to the world of Partial Differential Equations by Professor Long-Wei Lin ten years ago at Zhongshan University. His thesis adviser, Professor Blake Temple, also encouraged his interest in the subject when he was working on his PhD at the University of California. However, it is Professor Liu who Dr Yang says has been instrumental in helping him achieve his outstanding results. The two mathematicians have worked together on several research papers and presented their findings together at a number of conferences. It was Professor Liu who recommended Dr Yang for the Morningside prize. "Dr Yang's work solved an important problem," says Professor Liu. "Many mathematicians have tried to arrive at a well-posedness theory for the Hyperbolic Conservation Laws since the eighteenth century, but all previous attempts have been unsuccessful." Professor Liu says that Dr Yang has two important qualities needed by a good researcher. "First, he just goes at the work and sticks with it. He was working on this particular project for three years before he came up with his final results. Second, he has original ideas, as is shown by the fact that he alone has come up with the beautiful idea of the entropy functional. I cannot explain why he has these ideas, or where they come from, but what is important is that they come to him!" Practical applications of Dr Yang's research include helping in product design and formulating a mathematical model on which theoretical computations can be carried out. "The fact that there now exists a well-posedness theory for equations like Eular's means that equations can be relied upon much more than before by physicists." say Professor Liu. Dr Yang is delighted with the medal, as he feels that his work is now being appreciated by the mathematical community at large. In the future, he intends to consider three problems. "One is the multi-dimensional problem," he says. "The second problem concerns the singularities of solutions to some systems, such as the vacuum problem and the transonic problem. The third will be to generalize the present theory in a move towards general systems and solutions."
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