On evolutionary equations related to skew-symmetric spatial operators
Abstract
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest a criteria of uniqueness of this semigroup. We also find a stronger criteria of uniqueness of generalized solutions. Applications to transport equations with solenoidal (and generally discontinuous) coefficients are given.
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