Computation and analysis of statistical solutions
- Statistical solutions of hyperbolic systems of conservation laws and incompressible Euler (Navier-Stokes) equations.
- Time-parameterized probability measures on function spaces.
- Mathematically rigorous description of Turbulent fluid flow.
- Convergent Monte-Carlo Finite Volume and Spectral Viscosity algorithms.
Selected Publications
U. S. Fjordholm, R. Käppeli, S. Mishra and E. Tadmor, Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws, Found. Comput. Math., 17 (3), 2017, 763-827.
U. S. Fjordholm, S. Lanthaler and S. Mishra, Statistical solutions of hyperbolic conservation laws I: Foundations, Arch. Rat. Mech. Anal.,226, 2017, 809-849.
U.S Fjordholm, K. O. Lye, S. Mishra and F. Weber, Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation, Math. Mod. Meth. Appl. Sci. (M3AS) , 30 (3), 2020.
S. Lanthaler, S. Mishra and C. Pares Pulido, Statistical solutions of the incompressible Euler equations, Math. Mod. Meth. Appl. Sci. (M3AS) , 2021, to appear, available from ArXiv 1909:06615.