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Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations
Global weak solutions Vlasov-Fokker-Planck Navier-Stokes system of equations
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2015/10/15
We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov-FokkerPlanck equation coupled to compressible Navier-Stokes equ...
Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations
global strong solutions one-dimensional compressible Navier-Stokes equations
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2015/10/15
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. It is a well known fact that if the initial datum are smooth and the initial density is bounded by below by a posi...
Existence of solutions for a higher order non-local equation appearing in crack dynamics
Hydraulic fractures Higher order equation Non-local equation Thin film equation Non-negative solutions periodic Hilbert transform
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2015/10/15
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
Existence and regularity of extremal solutions for a mean-curvature equation
Mean curvature minimal solution semi-stable solution extremal solution regularity
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2015/10/15
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
Limit of fluctuations of solutions of Wigner Equation
fluctuations of solutions Wigner Equation
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2015/7/14
We consider fluctuations of the solution W ε(t, x, k) of the Wigner equation, which describes energy evolution of a solution of the Schr¨odinger equation with a random white noise in time potential. T...
Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential
Fluctuations of solutions Wigner equation Ornstein-Uhlenbeck potential
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2015/7/14
We consider energy fluctuations for solutions of the Schrodinger equation with an OrnsteinUhlenbeck random potential when the initial data is spatially localized. The limit of the fluctuations of the ...
Asymptotics of the solutions of the stochastic lattice wave equation
solutions stochastic lattice wave equation
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2015/7/14
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3
Allen-Cahn Equation Embedded Minimal Surfaces Finite Total Curvature in R3
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2015/4/3
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3.
Multiple positive solutions for semilinear Schrodinger equations
Multiple positive solutions semilinear Schrodinger equations
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2015/4/3
Multiple positive solutions for semilinear Schrodinger equations.
Nontrivial solutions for a a class of singular problems
Nontrivial solutions a a class of singular
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2015/4/3
Nontrivial solutions for a a class of singular problems.
A continuum of periodic solutions to the planar four-body problem with various choices of masses
periodic solutions planar four-body problem various choices of masses
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2015/3/18
A continuum of periodic solutions to the planar four-body problem with various choices of masses.
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems
Lambert’s theorem convex optimization minimizing solutions n-body problems
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2015/3/18
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems.
Regularity of Holder continuous solutions of the supercritical quasi-geostrophic equation
the 2D quasi-geostrophic equation supercritical dissipation regularity weak solutions
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2014/4/4
We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1/2) dissipation (−∆)α: If a Leray-Hopf weak solution is H¨older continuous θ...
GLOBAL SOLUTIONS FOR THE GRAVITY WATER WAVES SYSTEM IN 2D
GLOBAL SOLUTIONS THE GRAVITY WATER WAVES SYSTEM 2D
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2014/4/3
We consider the gravity water waves system in the case of a one dimensional interface, for suf- ficiently smooth and localized initial data, and prove global existence of small solutions. This i...
Existence of three solutions to a non-homogeneous multi-point BVP of second order differential equations
Second order differential equation with p-Laplacian generalized Sturm-Liouville boundary value problem fixed point theorem in cone
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2011/4/6
This paper is concerned with a non-homogeneous multi-point boundary value problem of second order differential equation with one-dimensional p-Laplacian. Using multiple fixed point theorems, sufficien...