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- W3102500984 abstract "We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on the compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropy flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multidimensional steady compressible fluids. We then analyze the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations." @default.
- W3102500984 created "2020-11-23" @default.
- W3102500984 creator A5018452636 @default.
- W3102500984 date "2015-08-07" @default.
- W3102500984 modified "2023-09-26" @default.
- W3102500984 title "Weak continuity and compactness for nonlinear partial differential equations" @default.
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- W3102500984 doi "https://doi.org/10.1007/s11401-015-0973-x" @default.
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