Title: An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions Show Chinese title

Title: 一个在二维空间中的双曲系统不适定的柯西问题

Abstract: The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed. Show Chinese abstract

Abstract: 非线性守恒定律的弱解理论在标量方程的情况下已经得到了充分的发展[3]，以及在一维双曲系统的情况下[1, 2]。 然而，对于多空间维数的系统，即使柯西问题解的全局存在性仍然是一个具有挑战性的开放问题。 在本文中，我们构造了一个反例，表明即使对于一类简单的双曲系统，在二维空间中柯西问题也可能不适定。