A structure-preserving discretization of incompressible Euler and Navier-Stokes equations using discrete exterior calculus that enforces exact conservation and excludes dissipative weak solutions above the Onsager threshold.
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SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.
The authors establish pathwise non-uniqueness for stochastic incompressible Euler equations with a passive tracer in dimensions d >= 2 by constructing infinitely many global weak solutions to equivalent random PDEs using the Baire category method, extending prior deterministic results to arbitrary 0
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Exact conservation and the Onsager threshold: a discrete exterior calculus theory for incompressible Navier-Stokes Equations
A structure-preserving discretization of incompressible Euler and Navier-Stokes equations using discrete exterior calculus that enforces exact conservation and excludes dissipative weak solutions above the Onsager threshold.
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Stein Variational Gradient Descent dynamics for highly concentrated kernels
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.
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Non-uniqueness for the stochastic incompressible Euler equations with a passive tracer
The authors establish pathwise non-uniqueness for stochastic incompressible Euler equations with a passive tracer in dimensions d >= 2 by constructing infinitely many global weak solutions to equivalent random PDEs using the Baire category method, extending prior deterministic results to arbitrary 0