共查询到20条相似文献,搜索用时 102 毫秒
1.
David Ruiz 《Archive for Rational Mechanics and Analysis》2010,198(1):349-368
This paper is motivated by the study of a version of the so-called Schrödinger–Poisson–Slater problem: $- \Delta u + \omega u + \lambda \left( u^2 \star \frac{1}{|x|} \right) u=|u|^{p-2}u,$ where ${u \in H^{1}(\mathbb {R}^3)}This paper is motivated by the study of a version of the so-called Schr?dinger–Poisson–Slater problem:
- Du + wu + l( u2 *\frac1|x| ) u=|u|p-2u,- \Delta u + \omega u + \lambda \left( u^2 \star \frac{1}{|x|} \right) u=|u|^{p-2}u, 相似文献
2.
Tobias Hansel 《Journal of Mathematical Fluid Mechanics》2011,13(3):405-419
We consider the equations of Navier–Stokes modeling viscous fluid flow past a moving or rotating obstacle in
\mathbb Rd{\mathbb R^d} subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity
vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In
order to use L
p
-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an
unbounded drift term. We prove that the linearized problem in
\mathbb Rd{\mathbb R^d} is solved by an evolution system on
Lps(\mathbb Rd){L^p_{\sigma}(\mathbb R^d)} for 1 < p < ∞. For this we use results about time-dependent Ornstein–Uhlenbeck operators. Finally, we prove, for p ≥ d and initial data
u0 ? Lps(\mathbb Rd){u_0\in L^p_{\sigma}(\mathbb R^d)}, the existence of a unique mild solution to the full Navier–Stokes system. 相似文献
3.
In this paper, we consider v(t) = u(t) − e
tΔ
u
0, where u(t) is the mild solution of the Navier–Stokes equations with the initial data
u0 ? L2(\mathbb Rn)?Ln(\mathbb Rn){u_0\in L^2({\mathbb R}^n)\cap L^n({\mathbb R}^n)} . We shall show that the L
2 norm of D
β
v(t) decays like
t-\frac |b|-1 2-\frac n4{t^{-\frac {|\beta|-1} {2}-\frac n4}} for |β| ≥ 0. Moreover, we will find the asymptotic profile u
1(t) such that the L
2 norm of D
β
(v(t) − u
1(t)) decays faster for 3 ≤ n ≤ 5 and |β| ≥ 0. Besides, higher-order asymptotics of v(t) are deduced under some assumptions. 相似文献
4.
Giovany M. Figueiredo Marcelo F. Furtado 《Journal of Dynamics and Differential Equations》2012,24(1):13-28
We consider the quasilinear problem
|