Global Regular Solutions for the Dynamic Antiplane Shear Problem in Nonlinear Viscoelasticity.
Global regular solutions to the Navier-Stokes equations in a cylinder
The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to and the gradient of the pressure to . We prove the existence of solutions without any restrictions on the lengths of the...
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 inhomogeneous incompressible Navier-Stokes equations with damping
This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids.
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.
Global regularity of the ...-Neumann problem on circular domains.
Global regularity of the solutions to the capillarity problem
Global representations of the Schrödinger equation with singular potential
We study the representation theory of the solution space of the one-dimensional Schrödinger equation with singular potential V λ(x) = λx −2 as a representation of . The subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. By studying the subspace of K-finite vectors in this space, a distinguished family of potentials, parametrized by the triangular numbers is shown to generate a global representation of ⋉ H 3, where H...
Global Schauder estimates for a class of degenerate Kolmogorov equations
We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...
Global self-similar solutions of a class of nonlinear Schrödinger equations.
Global smooth solutions of some quasi-linear hyperbolic systems with large data
Global smooth solutions of the SPIN polarized transport equation.
Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.
Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices.
Global solution of mixed problem for a certain system of nonlinear conservation laws
Global solution of optimal shape design problems.
Global Solution of the System of Wave and Klein-Gordon Equations.