اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدWellposedness of Cauchy problem for the Fourth Order Nonlinear Schrodinger Equations in Multi-dimensional Spaces
156
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrodinger equations ipartial_t u=-epsDelta u+Delta^2 u+P((partial_x^alpha u)_{abs{alpha}ls 2}, (partial_x^alpha bar{u})_{abs{alpha}ls 2}),quad tin Real, xinReal^n, where $epsin{-1,0,1}$, $ngs 2$ denotes the spatial dimension and $P(cdot)$ is a polynomial excluding constant and linear terms.
قيم البحث
اقرأ أيضاً
We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrodinger equation. By considering the renormalized equation, we extend the quasi-invariance results
in [30, 27] to Sobolev spaces of negative regularity. Our proof combines the approach introduced by Planchon, Tzvetkov, and Visciglia [35] with the normal form approach in [30, 27].
This paper is concerned with solution in H{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic s
patial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional H{o}lder spaces for them and give some inequalities among these H{o}lder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.
In this paper, we investigate the one-dimensional derivative nonlinear Schrodinger equations of the form $iu_t-u_{xx}+ilambdaabs{u}^k u_x=0$ with non-zero $lambdain Real$ and any real number $kgs 5$. We establish the local well-posedness of the Cauch
y problem with any initial data in $H^{1/2}$ by using the gauge transformation and the Littlewood-Paley decomposition.
We consider the Cacuhy problem for a viscous compressible rotating shallow water system with a third-order surface-tension term involved, derived recently in the modelling of motions for shallow water with free surface in a rotating sub-domain. The g
lobal existence of the solution in the space of Besov type is shown for initial data close to a constant equilibrium state away from the vacuum. Unlike the previous analysis about the compressible fluid model without coriolis forces, the rotating effect causes a coupling between two parts of Hodges decomposition of the velocity vector field, additional regularity is required in order to carry out the Friedrichs regularization and compactness arguments.
We consider nonlinear Schr{o}dinger equations in Fourier-Lebesgue and modulation spaces involving negative regularity. The equations are posed on the whole space, and involve a smooth power nonlinearity. We prove two types of norm inflation results.
We first establish norm inflation results below the expected critical regularities. We then prove norm inflation with infinite loss of regularity under less general assumptions. To do so, we recast the theory of multiphase weakly nonlinear geometric optics for nonlinear Schr{o}dinger equations in a general abstract functional setting.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
