138 research outputs found
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term
We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type
L u + V u= 0,
where L is a linear second order hypoelliptic operator and V
belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem
On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in {\mathbb{R}^{3}}
In this paper, we establish a blow-up criterion of strong solutions to the 3D incompressible magnetohydrodynamics equations including two nonlinear extra terms: the Hall term (quadratic with respect to the magnetic field) and the ion-slip term (cubic with respect to the magnetic field). This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015)
ESTIMATES OF THE DERIVATIVES OF MINIMIZERS OF A SPECIAL CLASS OF VARIATIONAL INTEGRALS
The note concerns on some estimates in Morrey Spaces for the derivatives of local minimizers of variational integrals of the form where the integrand has the following special form where and symmetric positive definite matrices. We are not assuming the continuity of and with respect to . We suppose that and are in the class
PAC Fields over Finitely Generated Fields
We prove the following theorem for a finitely generated field : Let be
a Galois extension of which is not separably closed. Then is not PAC
over .Comment: 7 pages, Math.
Existence of radial solutions for a p ( x ) -Laplacian Dirichlet problem
AbstractIn this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized
p
(
x
)
-Laplacian problem
−
Δ
p
(
x
)
u
+
R
(
x
)
u
p
(
x
)
−
2
u
=
a
(
x
)
|
u
|
q
(
x
)
−
2
u
−
b
(
x
)
|
u
|
r
(
x
)
−
2
u
with Dirichlet boundary condition in the unit ball in
R
N
(for
N
≥
3
), where a, b, R are radial functions
A regularity criterion in multiplier spaces to Navier-Stokes equations via the gradient of one velocity component
In this paper, we study regularity of weak solutions to the incompressible
Navier-Stokes equations in . The main goal is to
establish the regularity criterion via the gradient of one velocity component
in multiplier spaces.Comment: 9 pages. arXiv admin note: text overlap with arXiv:2005.1401
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