相关论文: Local strong solution to General Landau-Lifshitz-B…
In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on $m$-dimensional closed Riemannian manifold and prove that it admits a unique local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial data is…
In this paper, we focus on the existence of strong solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation. We construct a new combination of Bourgain space and Lebesgue space where linear and…
We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space $\dot{B}_{2,1}^{\frac{3}{2}}$. Utilizing a new commutator estimate, we establish the local…
We demonstrate the existence of stable time dependent solutions of the Landau-Lifshitz model with a constant external magnetic field. We find such solutions in all topological sectors, including N=0. We discuss some of their properties.
In this paper, we mainly consider the global solvability of smooth solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation in the Morrey space. We derive the covariant complex Ginzburg-Landau equation…
In this work, we prove the existence of local convex solution to the degenerate Hessian equation
The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate…
The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB…
In this paper, we are concerned with the local well-posedness of the initial-boundary value problem for complex Ginzburg-Landau (CGL) equations in bounded domains. There are many studies for the case where the real part of its nonlinear…
We study local existence for the Boltzmann equation near a global Maxwellian.
This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space $\mathbb{R}^3$. The study first demonstrates the existence and uniqueness of global strong solutions using the weak…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
In this paper we study Newton's method for solving generalized equations in Banach spaces. We show that under strong regularity of the generalized equation, the method is locally convergent to a solution with superlinear/quadratic rate. The…
In this paper, complex Ginzburg-Landau (CGL) equations with superlinear growth terms are studied. We discuss the local well-posedness in the energy space H1 for the initial-boundary value problem of the equations in general domains. The…
In this paper, a type of integrable evolution equation--the generalized Landau-Lifshitz equation into $S^n$ is considered. We deal with this equation from a geometric point of view by rewriting it in a geometric form. Through the geometric…
We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of $\mathbb{R}^2$. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for…
The aim of this article is to show a local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equation for arbitrarily large initial data. The goal is reached by $L^p$-theory for linearized equations which…
We prove local solvability of the Poisson equation with a positive or negative right-hand side for closed $G_2$-structures.
We consider here the local existence of strong solutions for the Zakharov-Kuznestov (ZK) equation posed in a limited domain (0,1)_{x}\times(-pi /2, pi /2)^d, d=1,2. We prove that in space dimensions 2 and 3, there exists a strong solution…
The existence and uniqueness of local in time strong solution with large initial data for the three-dimensional compressible viscoelastic fluid is established. The strong solution has weaker regularity than the classical solution. The…