相关论文: Stochastic conservation laws: weak-in-time formula…
We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…
A stochastic description of solutions of the Navier-Stokes equation is investigated. These solutions are represented by laws of finite dimensional semi-martingales and characterized by a weak Euler- Lagrange condition. A least action…
In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], where the pointwise internal…
In this paper, we study stability properties of solutions to scalar conservation laws with a class of non-convex fluxes. Using the theory of $a$-contraction with shifts, we show $L^2$-stability for shocks among a class of large…
We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely…
We introduce the notion of pathwise entropy solutions for a class of degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity and fluxes with rough time dependence and prove their well-posedness. In the case of Brownian…
Entropy functions played a key role in the development of mathematical theory for hyperbolic conservation laws. The notion of entropy, which is intimately connected with symmetry, is an extension \emph{imposed} on nonlinear systems of…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…
We propose a new sufficient non-degeneracy condition for the strong precompactness of bounded sequences satisfying the nonlinear first-order differential constraints. This result is applied to establish the decay property for periodic…
We consider multidimensional conservation laws perturbed by multiplicative L\'{e}vy noise. We establish existence and uniqueness results for entropy solutions. The entropy inequalities are formally obtained by the It\^{o}-L\'{e}vy chain…
We study one-dimensional conservation law. We develop a simple numerical method for computing the unique entropy admissible weak solution to the initial problem. The method basis on the equal-area principle and gives the solution for given…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
We establish a general nonlocal approximation principle for the entropy solutions of scalar conservation laws on $\mathbb{R}$. More precisely, we show that the entropy solution to a nonnegative initial datum can be obtained as a weak-star…
A weak invariant of a stochastic system is defined in such a way that its expectation value with respect to the distribution function as a solution of the associated Fokker-Planck equation is constant in time. A general formula is given for…
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair $(\eta(u),q(u))$ with…
Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we…