Related papers: Well-posedness for the Majda-Biello system on the …

A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

In this article we develop the local wellposedness theory for quasilinear Maxwell equations in $H^m$ for all $m \geq 3$ on domains with perfectly conducting boundary conditions. The macroscopic Maxwell equations with instantaneous material…

In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a…

We consider the quadractic NLS posed on a bidimensional compact Riemannian manifold $(M, g)$ with $ \partial M \neq \emptyset$. Using bilinear and gradient bilinear Strichartz estimates for Schr\"odinger operators in two-dimensional compact…

This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…

In this paper we study the fifth order Kadomtsev--Petviashvili II (KP--II) equation on the upper half-plane $U=\{(x,y)\in \R^2: y>0\}$. In particular we obtain low regularity local well-posedness using the restricted norm method of Bourgain…

In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the $L^2$-based Sobolev spaces. We derive bilinear estimate in a…

The initial-value problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system was recently introduced in [4]. It is numerically shown to be stable and a good approximation to the…

We consider the global well-posedness for the Cauchy probelem of the Kawahara equation which is one of the fifth order KdV type equations. We first establish the local well-posedness in a more suitable function space for the global…

Local well-posedness for the Dirac - Klein - Gordon equations is proven in one space dimension, where the Dirac part belongs to H^{-{1/4}+\epsilon} and the Klein - Gordon part to H^{{1/4}-\epsilon} for 0 < \epsilon < 1/4, and global…

Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…

We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields…

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails. A motivational example of a problem…

We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures.…

We consider some parabolic equations which are model problems for a variety of nonlinear generalizations to the Black-Scholes equation of mathematical finance. In particular, we prove local well-posedness for the Cauchy problem with initial…

We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\R^2))^4$, $s>3/2$, using…

We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore. Our result involves fine a priori estimates of the moving boundary evolution, Banach…

Projection stabilisation applied to general Lagrange multiplier finite element methods is introduced and analysed in an abstract framework. We then consider some applications of the stabilised methods: (i) the weak imposition of boundary…

In this paper we study the regularity properties of the "good" Boussinesq equation on the half line. We obtain local existence, uniqueness and continuous dependence on initial data in low-regularity spaces. Moreover we prove that the…