Develops local classical solution theory for stochastic Euler equations with pseudo-differential Stratonovich/Itô and Marcus noise and establishes a criterion for invariant probability measures that resolves Shirikyan's open problem in the damped incompressible case across dimensions.
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Existence, uniqueness, improved regularity, and pathwise exponential convergence to zero are established for strong solutions of stochastic curve shortening flow driven by transport-type pure jump Lévy noise.
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Stochastic Euler Equations with Pseudo-differential Noise: Continuous and Discontinuous Perturbations in Compressible and Incompressible Flows
Develops local classical solution theory for stochastic Euler equations with pseudo-differential Stratonovich/Itô and Marcus noise and establishes a criterion for invariant probability measures that resolves Shirikyan's open problem in the damped incompressible case across dimensions.
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Stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise
Existence, uniqueness, improved regularity, and pathwise exponential convergence to zero are established for strong solutions of stochastic curve shortening flow driven by transport-type pure jump Lévy noise.