Related papers: A Variational Principle for Dissipative Fluid Dyna…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant solutions. Even under the presence of infinitely many…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…
Hamiltonian variational principles provided, since 60s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by…
We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
We developed the spacetime-covariant Hamilton principle for barotropic flows of a perfect fluid in the external axial-vector potential conjugate to the helicity current. Such flows carry helicity, a chiral imbalance, controlled by the axial…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an…
The conditions of existence of extra mass flux in single component dissipative non-relativistic fluids are clarified. By considering Galilean invariance we show that if total mass flux is equal to total momentum density, then mass,…
We show that the ideal (nondissipative) form of the dynamical equations for the Lipps-Hemler formulation of the anelastic fluid model follow as Euler-Poincar\'{e} equations, obtained from a constrained Hamilton's principle expressed in the…