相关论文: Uniform stability estimates for constant-coefficie…

We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…

The paper is devoted to investigating the well-posedness, stability and large-time behavior near the hydrostatic balance for the 2D Boussinesq equations with partial dissipation. More precisely, the global well-posedness is obtained in the…

We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…

Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an $L^{2}$-setting of monomially weighted spaces. A mathematical framework is developed which…

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

We establish the global existence of a class of strongly coupled parabolic systems. The necessary apriori estimates will be obtained via our new approach to the regularity theory of parabolic scalar equations with integrable data and new…

We study the stability of one-dimensional linear lattice Boltzmann schemes for scalar hyperbolic equations with respect to boundary data. Our approach is based on the original raw algorithm on several unknowns, thereby avoiding the need for…

We consider the Schr\"odinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we get strong well-posedness…

We study the Muskat problem for one fluid or two fluids, with or without viscosity jump, with or without rigid boundaries, and in arbitrary space dimension $d$ of the interface. The Muskat problem is scaling invariant in the Sobolev space…

This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…

For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space $B^{\alpha,\infty}_q$ and satisfying a one-sided bound condition are unique within the class of dissipative…

In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…

The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…

The stability of the system is an important part of the research on differential dynamical systems. This paper considers a pointwise hyperbolic system defined on a connected open subset N of a compact smooth Riemannian manifold M. The…

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…

Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…

In this paper we present an improvement of [Math. Ann. 345 (2009), 213--243], where the authors proved a result concerning continuous dependence for backward parabolic operators whose coefficients are Log-Lipschitz in $t$ and $C^2$ in $x$.…

We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

We consider the forced surface quasi-geostrophic equation with supercritical dissipation. We show that linear instability for steady state solutions leads to their nonlinear instability. When the dissipation is given by a fractional…