167 citations · 1.3k across the 78 of their papers we have counts for
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On the vanishing viscosity limit of statistical solutions of the incompressible Navier-Stokes equations
Ulrik Skre Fjordholm, Siddhartha Mishra, Franziska Weber
We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are pr…
On Bayesian data assimilation for PDEs with ill-posed forward problems
Samuel Lanthaler, Siddhartha Mishra, Franziska Weber
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Na…
On the conservation of energy in two-dimensional incompressible flows
S. Lanthaler, S. Mishra, C. Parés-Pulido
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underl…
Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on
E. Compaan, N. Tzirakis
In this paper we establish an almost optimal well-posedness and regularity theory for the Klein-Gordon-Schrödinger system on the half line. In particular we prove local-in-time wel…
Statistical solutions of hyperbolic conservation laws I: Foundations
Ulrik Skre Fjordholm, Samuel Lanthaler, Siddhartha Mishra
We seek to define statistical solutions of hyperbolic systems of conservation laws as time-parametrized probability measures on -integrable functions. To do so, we prove the equ…
Numerical methods with controlled dissipation for small-scale dependent shocks
Philippe G. LeFloch, Siddhartha Mishra
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit…