ترغب بنشر مسار تعليمي؟ اضغط هنا

Existence of axially symmetric weak solutions to steady MHD with non-homogeneous boundary conditions

101   0   0.0 ( 0 )
 نشر من قبل Shangkun Weng
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Shangkun Weng




اسأل ChatGPT حول البحث

We establish the existence of axially symmetric weak solutions to steady incompressible magnetohydrodynamics with non-homogeneous boundary conditions. The key issue is the Bernoullis law for the total head pressure $Phi=f 12(|{bf u}|^2+|{bf h}|^2)+p$ to a special class of solutions to the inviscid, non-resistive MHD system, where the magnetic field only contains the swirl component.



قيم البحث

اقرأ أيضاً

We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable con dition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.
77 - Shangkun Weng 2015
We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of $u_{th}$ and $ a {bf u}$, especially we show that $|u_{th} (r,z)|leq cleft(f{log r}{r}right)^{f 12}$ for any smooth axially symmetric D-solutions to the Navier-Stokes equations. These improvement are based on improved weighted estimates of $om_{th}$, integral representations of ${bf u}$ in terms of $bm{om}=textit{curl }{bf u}$ and $A_p$ weight for singular integral operators, which yields good decay estimates for $( a u_r, a u_z)$ and $(om_r, om_{z})$, where $bm{om}= om_r {bf e}_r + om_{th} {bf e}_{th}+ om_z {bf e}_z$. Another is the first decay rate estimates in the $Oz$-direction for smooth axially symmetric flows without swirl. We do not need any small assumptions on the forcing term.
90 - Wenjun Liu , Yadong Liu , Jun Yu 2020
We consider a fluid-structure interaction problem with Navier-slip boundary conditions in which the fluid is considered as a non-Newtonian fluid and the structure is described by a nonlinear multi-layered model. The fluid domain is driven by a nonlin ear elastic shell and thus is not fixed. To simplify the problem, we map the moving fluid domain into a fixed domain by applying an arbitrary Lagrange Euler mapping. Unlike the classical method by which we can consider the problem as its entirety, we utilize the time-discretization and split the problem into a fluid subproblem and a structure subproblem by an operator splitting scheme. Since the structure subproblem is nonlinear, Lax-Milgram lemma does not hold. Here we prove the existence and uniqueness by means of the traditional semigroup theory. Noticing that the Non-Newtonian fluid possesses a $ p- $Laplacian structure, we show the existence and uniqueness of solutions to the fluid subproblem by considering the Browder-Minty theorem. With the uniform energy estimates, we deduce the weak and weak* convergence respectively. By a generalized Aubin-Lions-Simon Lemma proposed by Muha and Canic [J. Differential Equations {bf 266} (2019), 8370--8418], we obtain the strong convergence. Finally, we construct the test functions and pass the approximate weak formulation to the limit as time step goes to zero with the convergence results.
121 - Zhen Lei , Xiao Ren , Qi S Zhang 2019
An old problem asks whether bounded mild ancient solutions of the 3 dimensional Navier-Stokes equations are constants. While the full 3 dimensional problem seems out of reach, in the works cite{KNSS, SS09}, the authors expressed their belief that the following conjecture should be true. For incompressible axially-symmetric Navier-Stokes equations (ASNS) in three dimensions: textit{bounded mild ancient solutions are constant}. Understanding of such solutions could play useful roles in the study of global regularity of solutions to the ASNS. In this article, we essentially prove this conjecture in the special case that $u$ is periodic in $z$. To the best of our knowledge, this seems to be the first result on this conjecture without unverified decay condition. It also shows that periodic solutions are not models of possible singularity or high velocity region. Some partial result in the non-periodic case is also given.
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak solutions, we i ntroduce a new definition of solutions which allows to prove the existence of solution to the initial boundary value problems with non-zero initial and boundary values and non-homogeneous terms lying in some arbitrary negative-order Sobolev spaces. For strong solutions, we introduce an optimal compatibility condition and prove the existence of the solutions. We introduce also some sharp conditions guaranteeing the existence of solutions with more regularity in time and space.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا