Finite-time gradient blow-up is proven for conservation laws with source under weaker initial data conditions than Barlin (2023), with small compact support length promoting singularity formation.
Bärlin, Blow-up of solutions to relaxed compressible Navier-Stokes equa- tions in divergence form, preprint, arXiv: 2202.05634v1
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Solutions to the one-dimensional hyperbolic Navier-Stokes equations, hyperbolized by nonlinear Cattaneo and Maxwell-type relaxation, develop gradient blow-up because the system has two genuinely nonlinear eigenvalues.
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Gradient Catastrophe for Solutions to the Conservation Laws with Source Term
Finite-time gradient blow-up is proven for conservation laws with source under weaker initial data conditions than Barlin (2023), with small compact support length promoting singularity formation.
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Gradient Catastrophe for Solutions to the Hyperbolic Navier-Stokes Equations
Solutions to the one-dimensional hyperbolic Navier-Stokes equations, hyperbolized by nonlinear Cattaneo and Maxwell-type relaxation, develop gradient blow-up because the system has two genuinely nonlinear eigenvalues.