Results 1 to 10 of about 36,551 (156)
Local Well-Posedness to the Cauchy Problem for an Equation of the Nagumo Type [PDF]
The Scientific World Journal, 2022 In this paper, we show the local well-posedness for the Cauchy problem for the equation of the Nagumo type in this equation (1) in the Sobolev spaces Hsℝ. If D>0, the local well-posedness is given for s>1/2 and for s>3/2 if D=0.
Vladimir Lizarazo +2 more
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Local Well-Posedness for Relaxational Fluid Vesicle Dynamics [PDF]
Journal of Evolution Equations, 2018 We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument.
Köhne, Matthias, Lengeler, Daniel
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Local well-posedness of the generalized Cucker-Smale model with singular kernels
ESAIM: Proceedings and Surveys, 2014 In this paper, we study the local well-posedness of two types of generalized kinetic Cucker-Smale (in short C-S) equations. We consider two different communication weights in space with nonlinear coupling of the velocities, v | v |
Carrillo José A. +2 more
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Sharp local well-posedness for the "good" Boussinesq equation [PDF]
Journal of Differential Equations, 2012 In the present article, we prove the sharp local well-posedness and ill-posedness results for the "good" Boussinesq equation on $\mathbb{T}$; the initial value problem is locally well-posed in $H^{-1/2}(\mathbb{T})$ and ill-posed in $H^s(\mathbb{T})$ for
Bejenaru +23 more
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Local well posedness for a linear coagulation equation [PDF]
Transactions of the American Mathematical Society, 2009 In this paper we derive some a priori estimates for a class of linear coagulation equations with particle fluxes towards large size particles. The derived estimates allow us to prove local well posedness for the considered equations.
Escobedo, M., Velazquez, J. J. L.
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Local well-posedness for membranes in the light cone gauge [PDF]
Communications in Mathematical Physics, 2009 In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint.
A. Abrahams +40 more
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Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics
Mathematics, 2021 In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On
Kenta Oishi, Yoshihiro Shibata
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Local well-posedness of a nonlocal Burgers’ equation [PDF]
Involve, a Journal of Mathematics, 2016 In this paper, we explore a nonlocal inviscid Burgers’ equation. Fixing a parameter h, we prove existence and uniqueness of the local solution of the equation ut +(u(x + h,t) ± u(x − h,t))ux = 0 with given periodic initial condition u(x,0) = u0(x). We also explore the blow-up properties of the solutions to this Cauchy problem, and show that there exist
Goodchild, Sam, Yang, Hang
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Local Well-Posedness for the Magnetohydrodynamics in the Different Two Liquids Case
Mathematics, 2022 We consider the free boundary problem of MHD in the multi-dimensional case. This problem describes the motion of two incompressible fluids separated by a closed interface under the action of a magnetic field.
Elena Frolova, Yoshihiro Shibata
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Local well-posedness for quasi-linear problems: A primer
Bulletin of the American Mathematical Society, 2022 Proving local well-posedness for quasi-linear problems in partial differential equations presents a number of difficulties, some of which are universal and others of which are more problem specific. On one hand, a common standard for what well-posedness should mean has existed for a long time, going back to Hadamard.
Ifrim, Mihaela, Tataru, Daniel
openaire +3 more sources