Sentence examples for a low regularity from inspiring English sources

Remark 4.2 Theorem 3.5 ensures that there exists a low regularity solution for (4.1).

In Section 4, an optimal-order weighted norm error analysis with a low regularity requirement for the optimal control problem is discussed.

In Section 2, we first recall the standard definition of weak solutions to the MHD system and give a stability results for the low regularity of the driving force, then we exploit it and show the existence of weak solutions for system (1.5 - 1.8 1.5 - 1.8ixed (irregular) force.

In this paper, we first prove the existence and uniqueness of a solution in Besov spaces for model (1.3a - 1.3d 1.3a - 1.3degularity initial data, withh is a matter of interest in the mathematicalownalysis, as well as the existence of solution, stability and spatial patteregularity

Stochastic differential equations (SDEs) driven by Brownian motion W and an additional deterministic path η of low regularity (so called "mixed SDEs") have been well-studied.

By a microlocal complex scaling constructed using suitable low regularity microlocal weights Sjöstrand [240] similarly localized resonant states to an ( sqrt{h} ) neighbourhood of the trapped set and hence was able to prove bounds of the form (3.54).

As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the modulation spaces, assuming a nonlinearity of analytic type.

Moreover, we present a sufficient condition which guarantees the existence of low regularity solutions for the generalized Camassa-Holm equation by the method of energy estimate.

The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions.

Ai and Gui [9] presented an algorithm for the inverse scattering problem associated to the Dullin-Gottwald-Holm equation and derived a sufficient condition which guarantees the existence of low regularity solutions for the generalized Dullin-Gottwald-Holm equation.

We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov Poisson Fokker Planck system with small non-linear term but with a possibly large exterior confining potential in dimension d= 2 and d="3.