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math.AP2019
Renormalization of stochastic continuity equations on Riemannian manifolds
Luca Galimberti, Kenneth H. Karlsen
We consider the initial-value problem for stochastic continuity equations of the form $$ \partial_t ρ+ \text{div}_h \left[ρ\left(u(t,x) + \sum_{i=1}^N a_i(x)\circ \frac{dW^i}{dt}\r…
math.AP2019
Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds
Luca Galimberti, Kenneth H. Karlsen
We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be we…