Rough solutions for the wave maps equation

By D. Tataru. 2005

136 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c84106e2e3030e4cff5ad72a75025b479deecf12

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Renormalization and blow up for charge one equivariant critical wave maps (2006, background): “he co-rotation 1 equivariant case has been recently provided in [Co]. We note that a fairly satisfactory understanding has been achieved for small-energy wave maps from R2+1 to general targets [Tao], [Tat], [Kri], as well as for rotationally invariant wave maps and general initial data [Chr-Tah], [S”
Low-regularity Schrödinger maps, II: global well-posedness in dimensions d ≥ 3 (2007, background): “Its direct analogue in the setting of wave maps is the work of Tataru [23] (see also [10], [12], [24], [21], [22], [11], [18], and [25] for other local and global well-posedness theorems for wave maps).”
On the formation of singularities in the critical $O(3)$ $\sigma$-model (2006, unknown): “In the case of dynamic solutions and the Cauchy problem, the only general understanding of the equations (3) that is yet available is for the local theory (see [18]) and the small data scale invariant (global) results of [37] (in the Besov case) and [36], [19], and [38] for the case of small energy.”
Concentration Compactness for Critical Wave Maps (2009, unknown): “Later results by Klainerman, Rodnianski [19], Nahmod, Stephanov, Uhlenbeck [36], Tataru [61], [60], and Krieger [23], [24], [25] considered other cases of targets by using similar methods as in Tao’s work.”
Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008, background): “Local solutions can also be constructed in significantly rougher function spaces than C: see [25], [74], [75], [76].”
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class (2008, methodology): “Some similar computations in the context of the global regularity problem for wave maps, but using an extrinsic regularisation method in place of the harmonic map heat flow, also appear in [23].”
GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R) (2003, methodology): “[26] (see also [13], [19]) and refined slightly in [ 28 ] for applications to persistence of regularity).”
Global existence and uniqueness of Schrödinger maps in dimensions d... 4 (2007, background): “Its direct analogue in the setting of wave maps is the work of Tao [25] (see also [14], [16], [27], [28], [26], [15], [22], [18], and [29] for other local and global existence (or well-posedness) theorems for wave maps).”
Global Regularity of Wave Maps from R2+1 to H2. Small Energy (2004, background): “Also, a recent preprint by D.Tataru [ 34 ] (which appeared when the research for this paper had been concluded) promises to solve the small-data case for n ≥ 2 and targets which can be uniformly isometrically imbedded into some Euclidean space.”
Regularity of Wave-Maps in Dimension 2 + 1 (2009, methodology): “Krieger, J., Schlag, W., Tataru, D.: Renormalization and blow up for charge one equivariant critical wave maps.”
Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, methodology): “The second tier of the article contains the proofs of all the results stated in Sections 2, 3, with the exception of those already proved in [29] and [33].”