ON THE WELL-POSEDNESS OF WEAK SOLUTIONS

• 作者: Taiping Liu
• 来源期刊: 应用数学年刊:英文版
• 学科: 数学
• 关键词: nonlinear PARTIAL DIFFERENTIAL EQUATIONS WELL-POSEDNESS theory WEAK solutions
• 年，卷（期）: 2019,（3）
• 页码范围: 309-316
• 页数: 8页
• 分类号: O17

摘要

This is to comment on the well-posedness of weak solutions for the initial value problem for partial differential equations.In recent decades,and particularly in recent years,there have been substantial progresses on construction by convex integration for the study of non-uniqueness of solutions for incompressible Euler equations,and even for compressible Euler equations.This prompts the question of whether it is possible to give a sense of well-posedness,which is narrower than the canonical Hadamard sense,so that the evolutionary equations are well-posed.We give a brief and partial review of the related results and offer some thoughts on this fundamental topic.