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On the Muskat problem: global in time results in 2D and 3D
Porous media incompressible ows uid interface global existence.
2014/4/3
This paper considers the three dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the uid interface. We also show global in time ex...
Global-in-time existence of perturbations around travelling-waves
nonlinear and nonlocal conservation law fractional anti-diffusive operator Duhamel formulation travelling-wave global-in-time existence
2011/8/22
Abstract: We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-...
A sufficiency class for global (in time) solutions to the 3D Navier-Stokes equations II
Global (in time) 3D-Navier-Stokes Equations
2010/12/7
In this paper, we simplify and extend the results of [GZ] to in-clude the case in which = R3. Let [L2(R3)]3 be the Hilbert space of square integrable functions on R3 and let H[R3]3 =: H be the comple...
Fundamental Solution Global in Time for a Class of Schrödinger Equations with Time-Dependent Potentials
Schrö dinger equation fundamental solution Fourier integral operators long-range potentials scattering theory
2008/11/25
Fundamental solution for a Schrödinger equation with a time-dependent potential of
long-range type is constructed. The solution is given as a Fourier integral operator with
a symbol uniformly b...
Global-in-time Uniform Convergence for Linear Hyperbolic-Parabolic Singular Perturbations
Parabolic equations Damped hyperbolic equations Singular perturbations
2007/12/12
We consider the Cauchy problem ${\varepsilon}{u_{\ep}}''+\delta{u_{\ep}}'+A{u_{\varepsilon}}=0,$ ${u_{\varepsilon}}(0)=u_0, $ ${u_{\varepsilon}}'(0)=u_{1},$ where ${\varepsilon}>0$, $\delta>0$, $H$ is...