Related papers: The Stokes phenomenon for certain partial differen…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with singularities. As a consequence, we obtain a direct,…
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…
This paper studies the convergence rates in $L^2$ and $H^1$ of Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any smoothness assumptions on the coefficients.
We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $\mathbb{CP}^1$ model by considering it as a specific decoupling limit of SQED$_2$ model. This approach involves using a $\mathbb{Z}_3$…
Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
As lensing of coherent astrophysical sources e.g. pulsars, fast radio bursts, and gravitational waves becomes observationally relevant, the mathematical framework of Picard-Lefschetz theory has recently been introduced to fully account for…
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…
Intersection numbers of Stokes polytopes living in complex projective space are computed using the techniques employed to find the inverse string KLT matrix elements in terms of intersection numbers of associahedra. To do this requires an…
We consider a family of Stokes waves on vorticity flow parameterized by a parameter. For large value of the parameter the Stokes waves approach the Stokes extreme wave. We prove that there are infinitely many subharmonic bifurcation points…
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…
We formulate a method for computing Stokes flow past a highly deformed sphere with arbitrarily defined surface velocity. The fundamental ingredient is an explicit extrapolation operator extending a velocity field from the surface of a…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…
In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of…
A stochastic theory is presented for a quantum vortex that is expected to occur in superfluids coated on two dimensional sphere $ {\rm S}^2 $. The starting point is the canonical equation of motion (the Kirchhoff equation) for a point…
We derive the explicit analytic expression for the Stokes' drift in one dimension in the presence of a dichotomic Markov forcing. For small amplitudes of the forcing, the drift is enhanced, but the enhancement is reduced with increasing…
In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…