Related papers: Well-posedness Properties for a Stochastic Rotatin…
In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
We consider a nonlinear fourth order in space partial differential equation arising in the context of the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We use the theory of operator semigroups in…
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L\'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D…
We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device is reformulated as a transmission problem related to the…
Properties of stochastic systems are defined by the noise type and deterministic forces acting on the system. In out-of-equilibrium setups, e.g., for motions under action of L\'evy noises, the existence of the stationary state is not only…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund…
We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced by a Lennard-Jones interaction. In addition to the pairwise…
The well-posedness for SDEs with singularity in both space and distribution variables is derived, where the interacting drift term is bounded and Lipschitz continuous under total variation distance and the diffusion term is allowed to be…
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…
This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the…
In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in $H_x^1\times H_x^1$. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear…
We prove the global well-posedness of the one-dimensional Navier-Stokes-Korteweg equations driven by a stochastic multiplicative noise. The analysis is performed for the general case of capillarity and viscosity coefficients $k(\rho)=…
We study the focusing $L^2$-critical and supercritical stochastic nonlinear Schr\"odinger equation subject to additive or multiplicative noise. We investigate global or long time behavior of solutions in $H^1$, which would correspond to…
We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…
Oral Glucose Tolerance Test (OGTT) is one of many way to produce data in the study of the diabetes dynamic. In a recent paper [1.]:\textit{ Estimating insulin sensitivity and $ \beta $-cell function from the oral glucose tolerance test:…