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This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…
We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations.
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In this paper, we study the partial differential equation on the circle that was heuristically obtained by Steinerberg [32] on the real line and which represents the evolution of the density of the roots of polynomials under…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…
We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
This work is the third part of a program initiated in arXiv:2111.13258, arXiv:2302.06571 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…
In this paper we deal with parabolic variational inequalities of Navier-Stokes type with time-dependent constraints on velocity fields, including gradient constraint case. One of the objectives of this paper is to propose a weak variational…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
In the class of the so called non-dynamic Fractional Obstacle Problems of parabolic type, it is shown how to obtain higher regularity as well as optimal regularity of the space derivatives of the solution. Furthermore, at free boundary…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…