Generic singularities for 2D pressureless flows  

作　　者：Alberto Bressan Geng Chen Shoujun Huang 

机构地区：[1]Department of Mathematics,Penn State University,University Park,PA 16802,USA [2]Department of Mathematics,University of Kansas,Lawrence,KS 66045,USA [3]College of Mathematical Medicine,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Science China Mathematics》2025年第3期559-576,共18页中国科学(数学英文版)

基　　金：supported by U.S.National Science Foundation(Grant No.DMS2006884)(singularities and error bounds for hyperbolic equations);supported by U.S.National Science Foundation(Grant Nos.DMS-2008504 and DMS-2306258);supported by Zhejiang Normal University(Grant Nos.YS304222929 and ZZ323205020522016004)。

摘　　要：In this paper,we consider the Cauchy problem for pressureless gases in two space dimensions with the generic smooth initial data(density and velocity).These equations give rise to singular curves,where the mass has a positive density with respect to the 1-dimensional Hausdorff measure.We observe that the system of equations describing these singular curves is not hyperbolic.For analytic data,local solutions are constructed by using a version of the Cauchy-Kovalevskaya theorem.We then study the interaction of two singular curves in the generic position.Finally,for a generic initial velocity field,we investigate the asymptotic structure of the smooth solution up to the first time when a singularity is formed.

关 键 词：pressureless gases formation of singularities generic data Cauchy-Kovalevskaya theorem 

分 类 号：O175[理学—数学]