By Sam Krupa
For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to the compressible vortex sheet. We address all of these questions by using the lens of convex integration, a general method of constructing highly irregular and non-unique solutions to PDEs. Our proofs involve computer-assistance.
Co-authors: László Székelyhidi, Jr.
By Stephen Griffies
By Catherine Sulem
By Richard Bamler
By Richard Bamler
By Richard Bamler
By Richard Bamler
By Kenji Nakanishi
