8 papers
Stochastic Euler Equations with Pseudo-differential Noise: Continuous and Discontinuous Perturbations in Compressible and Incompressible Flows
Kenneth. H. Karlsen, Hao Tang, Feng-Yu Wang
We study stochastic Euler equations in compressible and incompressible regimes, on the whole space and the torus, driven by mixed multiplicative noise: continuous Stratonovich/Itô…
Structure-preserving LDG methods for linear and nonlinear transport equations with gradient noise
Thomas Christiansen, Kenneth H. Karlsen
We develop local discontinuous Galerkin (LDG) methods for conservation laws with heterogeneous stochastic fluxes, where the Stratonovich-driven transport terms may be linear or non…
Regularity of velocity averages in kinetic equations with heterogeneity
Marko Erceg, Kenneth H. Karlsen, Darko MitroviÄ
This study investigates the regularity of kinetic equations with spatial heterogeneity. Recent progress has shown that velocity averages of weak solutions in () are…
Velocity averaging under minimal conditions for deterministic and stochastic kinetic equations with irregular drift
Marko Erceg, Kenneth H. Karlsen, Darko MitroviÄ
This study investigates the compactness of velocity averages of sequences of solutions for a class of kinetic equations. The equations are exam…
Semi-discrete heat equations with variable coefficients and the parametrix method
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
We develop a parametrix approach for constructing solutions and establishing grid-size independent estimates for semi-discrete heat equations with variable coefficients. While the…
Upwind filtering of scalar conservation laws
Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen, Nils Henrik Risebro
We study a class of multi-dimensional non-local conservation laws of the form , where the standard local divergence $\operatorna…