Gain of regularity for a Korteweg-de Vries--Kawahara type equation.
Gain of regularity for equations of KdV type
General mixed problems for the KdV equations on bounded intervals.
Generalized Gevrey classes and multi-quasi-hyperbolic operators.
Generation of analytic semigroups by elliptic operators of second order in Hölder spaces
Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
Global and exponential attractors for a Caginalp type phase-field problem
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
Global attractor for the Navier-Stokes equations in a cylindrical pipe
Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.
Global Caccioppoli-type and Poincaré inequalities with Orlicz norms.
Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
Global Hölder estimates for equations of Monge-Ampère type.
Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that...
Global optimal regularity for the parabolic polyharmonic equations.
Global Regular Solutions for the Dynamic Antiplane Shear Problem in Nonlinear Viscoelasticity.
Global regularity for solutions of the minimal surface equation with continuous boundary values
Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity and with natural growth
In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for...
Global regularity for the 3D MHD system with damping
We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.
Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.
Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions.