相关论文: Local Well-posedness for the Kinetic MMT Model
Integration of machine learning (ML) models of unresolved dynamics into numerical simulations of fluid dynamics has been demonstrated to improve the accuracy of coarse resolution simulations. However, when trained in a purely offline mode,…
In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized…
Whether the quantum mechanics (QM) is non-local is an issue disputed for a long time. The violation of the Bell-type inequalities was considered as proving this non-locality. However, these inequalities are constructed on a class of local…
We study a moisture model for warm clouds that has been used by Klein and Majda as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the…
We investigate the stabilization of a locally coupled wave equations with only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty in this paper is that both the damping and the coupling coefficients are non smooth.…
Our aim in this paper is to study local rigidity for metrics defined on a compact manifold $M$ with boundary satisfying constant scalar curvature on $M$ and constant mean curvature on $\partial M$. We present some geometrical hypotheses…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
We consider the classical Yang-Mills system coupled with a Dirac equation in 3+1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This…
Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal…
The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability of a…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
We prove local well-posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose…
The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view,…
We study the stabilization issue of the Benjamin-Bona-Mahony (BBM) equation on a finite star-shaped network with a damping term acting on the central node. In a first time, we prove the well-posedness of this system. Then thanks to the…
We consider the initial-value problem for the bidirectional Whitham equation, a system which combines the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow-water nonlinearity. We prove local…
Time local well-posedness for the Maxwell-Schr\"odinger equation in the coulomb gauge is studied in Sobolev spaces by the contraction mapping principle. The Lorentz gauge and the temporal gauge cases are also treated by the gauge transform.
We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $\Omega$ with the specular reflection condition. Our result covers the case when $\Omega$ is a non-convex domain, e.g., solid…
In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the…
The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schr\"odinger equation and Klein-Gordon equation. These theories encompass both local and global well-posedness, as…
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…